Last summer, Antonia Steinberg heard chatter on her walkie-talkie that would make any camp director shiver: Two kids hadn’t shown up for the 10 p.m. “put-to-bed” curfew. Ms. Steinberg, then all of 22 and in her first summer as president of the camp, got into her car and drove in the darkness to search.

At the camp, Buck’s Rock in New Milford, Conn., sought out by generations of outside-the-box kids, put-to-bed is the only nonnegotiable scheduling requirement. At nearly all other times, campers are free to do what they want, when they want.

When the campers were finally spotted, outside the actors’ studio, one bolted toward the woods. Soon, the camper stopped running and, early the next morning, went home for a week to regroup.

“Sometimes it feels impossible, the amount of things going on all at once,” Ms. Steinberg said. “I sometimes think this is an impossible amount to carry on my shoulders.”

She first came to Buck’s Rock when she was 10, drawn by its arts resources and its Montessori approach, the same qualities that have attracted alumni like the actress Paz de la Huerta, Ezra Koenig of Vampire Weekend and Ben Cohen of Ben & Jerry’s.

Ms. Steinberg has returned every summer since, aging from camper to counselor in training (C.I.T.) to counselor, and now, president. “My grandmother always joked that someday I would run this place,” she said. That her grandmother is Diane von Furstenberg, the fashion designer and now busy philanthropist, helps to explain how a casual comment could turn out to be prophetic.

Ms. Steinberg has been grappling her whole life with the implications — and obligations — of her family’s celebrity and wealth. She is strikingly direct when discussing her family’s buying power. “It’s the truth,” she said. “It would be weird if I lied about it, and it would be a shame not to use it.”

And so, two years ago, with the camp in crisis, she decided to rescue her childhood refuge and transform it into a nonprofit. Forty-three percent of campers are now on partial or full scholarships, the camp said, so they might have the chance to experience summer as Ms. Steinberg always had.

‘Not a Babysitting Service’

In 1941, Dalton, the private school on the Upper East Side of Manhattan that was then all-girls, bought land in New Milford. The property was intended as a safe haven for its students to continue their education in case German bombs came to New York.

Within a couple of years, though, the site passed to the directorship of Ilse and Ernst Bulova, two refugees from Hitler’s Third Reich. The married couple were teachers who had fled their native Austria because of their political beliefs (socialist) and educational philosophy (Montessori).

They turned the property into a summer camp, but one that would be radically different from the “military style” summer camps they observed on their tour of the American Northeast. They ran Buck’s Rock camp for the next 32 years, putting campers to work growing vegetables, taking care of animals and helping to prepare meals.

“I was so unhappy in my childhood and so happy there,” said the writer Molly Jong-Fast, who attended Buck’s Rock in the 1990s. Her mother, the novelist Erica Jong, had also attended, back when it was a “socialist work camp,” Ms. Jong-Fast said. By the time Ms. Jong-Fast was a camper, the emphasis was on the arts.

“I loved to draw, I loved to do batik, I wrote for the newspaper,” she said. “You could do art in a low-key way. You didn’t have to be Picasso.”

The novelist Lionel Shriver was a counselor at Buck’s Rock for three summers in the early 1980s and remembers it affectionately.

“It was not a babysitting service. It had serious aspirations,” she said. “I taught at another camp, too. It was basically crayons and crepe paper, whereas Buck’s Rock took visual arts seriously.”

The day before camp opened this summer, counselors and C.I.T.s ran through their final tasks, checking the ragtag collection of cabins.

Ms. Steinberg sat outside the wood shop, her favorite place in camp to sit. “This was my haven,” she said, over the buzz of saws.

With the curly brown hair and watchful, wide-set eyes of the von Furstenberg women, Ms. Steinberg, now 23, spoke deliberately, as she greeted counselors and heads of shop as they passed by. They are all her employees now, but many have known her since she was 10.

“It’s hard because of my age to have a sense of authority, to develop it within myself, and for other people to see it and respect it,” Ms. Steinberg said.

She was born and raised mostly in Los Angeles. Her mother, Tatiana von Furstenberg, is a filmmaker, and her father, Russell Steinberg, is a performance artist.

She attended more than nine schools, including a small Montessori program in the San Fernando Valley and a boarding school in England. She finished high school by collecting credits at Los Angeles Community College.

But, from age 10, she went to New Milford every summer. “The one thing that was consistent was Buck’s Rock,” she said.

Campers are free to walk into any “shop” at any point in any day, except during meals, trying out glassblowing, metal welding, ceramics, batik, painting, woodwork, music, dance, performance, creative writing, photography and even radio broadcasting.

During her first summer as a camper, Ms. Steinberg made a pair of wooden clogs for her mother (her mother still has them). Over the years, she said, she “accidentally assembled a portfolio,” which she used in her application to Rhode Island School of Design, from which she graduated in 2022.

While Ms. Steinberg was still in college, the previous owner of Buck’s Rock, Noah Salzman, contacted her mother to see if a sale might be of interest to them. It was 2020, and the coronavirus pandemic was devastating the camp industry. For the first time in its long history, Buck’s Rock did not open for the summer. Mr. Salzman, an educator in San Francisco, whose tenure as owner had been rocky, recognized that the camp might shut down permanently, he said.

Ms. Steinberg recalled that when her mother first heard Mr. Salzman’s proposal, she thought that running a camp sounded like a “nightmare.”

“I knew the enormity of the undertaking,” Tatiana von Furstenberg said. “As her mother, I have had to be there as she’s been completely overwhelmed at times. When it started, she had had only 20 years on this earth.”

Since taking over, Ms. Steinberg’s list of problems has included: a lightning storm that fried the camp’s P.A. system; a camp chef who quit at the end of a lunch shift, blocked her number, and left her without anyone to cook dinner that night for roughly 450; the various black bears that wander by; the inevitable need to send certain campers — and counselors — packing.

But when Diane von Furstenberg heard about the potential acquisition of Buck’s Rock, she encouraged her granddaughter, invoking a family tenet: “There are no coincidences.”

Ms. Steinberg may not have instantly grasped all that would be required, but the timing of Mr. Salzman’s call was auspicious. She’d recently done a training program offered by the Gates Foundation called Next Gen, aimed at educating young, up-and-coming philanthropists. She finished the program before she turned 21, the age at which she would be eligible to join the board of the Diller-von Furstenberg Family Foundation (her stepgrandfather is Barry Diller).

Ms. Steinberg knows how all of this might sound: privileged young person gets handed a camp. “I’m very much aware of my position,” she said, “and I definitely feel a big sense of responsibility given my circumstances — and my experiences at Buck’s Rock.” She added that she didn’t think she would have done something so “crazy if I wasn’t some combination of naïve and confident.”

‘The Inmates Are Running the Asylum’

On opening day of camp this summer, Ms. Steinberg walked the grounds with a clipboard, as campers and their parents waited to check in. They clutched portable fans, toiletries and assorted musical instruments, and the vibe was low-key and democratic, even as Ethan Hawke was spotted by the lice-check station.

Jacob Abramovich, 13, from the Upper West Side, was back for his third summer. “I love sculpture, metalwork, welding, blacksmithing — anything with metal,” he said.

Heather Bancroft, a former Buck’s Rock camper, arrived from New Jersey to drop her two teenage children off. She could still remember Ernst Bulova in his 90s, walking through the camp, picking up garbage. “We were just teenagers, but we could understand this was a unique experience,” she said. “On the car ride up I said to my kids, ‘Do whatever you want to do this summer.’ Their lives are so regimented. To have the ability to decide how to spend your day, to have that freedom — that’s the magic.”

Ms. Bancroft walked her daughter to her cabin, where her bunk mates’ names adorned the door. In choosing bunks, campers specify which gender they identify as.

Back near check-in, a gaggle of laughing girls arrived together for their first summer at Buck’s Rock. They are students at Success Academy in the Far Rockaway neighborhood of Queens, and they each had won a scholarship to camp by writing about why they wanted to come. One girl, 12, said she had written about how, as a city kid, “I have many fears about nature, so I thought that camp could be a good opportunity to get rid of those.”

It was a psychological strategy Diane von Furstenberg could appreciate: Her own mother locked her in a closet to help her overcome her fear of the dark, she wrote in her memoir, “The Woman I Wanted to Be.” Her mother, Lily Nahmias, operated by the credo that “fear is not an option.” She survived Auschwitz at almost exactly the same age her great-granddaughter is now.

“This place is truly too special not to share,” Ms. Steinberg said. “Exclusivity is the antithesis of Buck’s Rock. And so for the camp to be prohibitively expensive and that being why it’s exclusive — it just felt wrong.”

She hired Alex Huber-Weiss, 32, another former camper, as director of development, and brought back Scott Kraiterman, 40, a former camper and now a psychologist at Dalton, as camp director. Mr. Kraiterman had been Ms. Steinberg’s counselor. “The inmates are running the asylum,” Ms. Huber-Weiss said with a laugh. If parents seem wary of Ms. Steinberg’s age, she directs them to Mr. Kraiterman.

When the camp reopened in 2022 — it was closed in 2021 — mice had taken over the main theater and destroyed the expensive stage lights.

But Ms. Steinberg had her new nonprofit infrastructure in place: a tiered tuition system, essentially “pay what you can,” to help remove barriers to access while still operating a sustainable business.

She said the camp cost just under $3 million a year to run. Tuition for both sessions (an eight-week stay) is $14,000, but many campers come on partial or full scholarships. Buck’s Rock now must secure donations and corporate partnerships to continue on as Ms. Steinberg intends. In the sewing shop, there are bolts of DVF jersey fabric donated by her grandmother.

The Diller-von Furstenberg foundation paid for the acquisition of the camp and also provided one year of funding. Buck’s Rock is currently operating at a deficit. Yet because of tuition proceeds, the family foundation and fund-raising, which brought in more than $500,000 in 2022, Ms. Steinberg said, “even if we operated in deficit for the next few years, we would still be all right.”

At the same time, she also raised the salaries of the counselors, to cast a wider net of who would be able to work there. One of those who joined as a guidance counselor during Ms. Steinberg’s first summer is Kellsie Mensah, 19. She said that she had been struck by the mental health challenges her campers faced. “I wasn’t expecting them to have so much anxiety,” she said.

Those experiences may sound familiar, what the surgeon general has called “the defining public health crisis of our time”: Among American children aged 10 to 19, rates of self-harm and suicide have soared in the last decade. Summer camps can pose special challenges for children who are not accustomed to being away from home, and away from their phones. (At Buck’s Rock, phones are taken away entirely for the first week, and then allowed for one hour each day.)

On a fiercely hot, humid day at the beginning of the second session, Ms. Steinberg walked down the long road that runs through the center of camp, from the dining hall down to the field where the vegetable garden was in full bloom. Here, on a wooden platform, campers were rehearsing for the summer’s big musical, “Spamalot.”

“Take a deep breath in and out, think about who you are and where you are, and get in touch with your internal ridiculousness,” Collins Hilton told his cast. Mr. Hilton, another former Buck’s Rock camper, is the head of drama.

The star of the show was Moxie Ewen, a 15-year-old from Los Angeles, and a fourth-generation Buck’s Rocker. In lace-up burgundy combat boots, she was rehearsing, with a serviceable British accent, her King Arthur, although her long blond tresses were more suggestive of Guinevere. “I command you in the name of the Knights of Camelot to open the doors of this sacred castle to which God himself has guided us!” King Arthur said, addressing her French peons. “I burst my pimples at you!” one of them shot back.

The camp has a long list of shows every summer, including two musicals, a dance concert and sketch comedy nights. During her first summer at camp, Ms. Steinberg decided to perform at the Rock Café, where campers showcase the music they have written. “I wrote a song about a breakup, about this girl who is kicking this guy out of her house and he just has to cope,” she said. “Maybe partially it was to do with my parents, I don’t know.”

Ms. Steinberg’s parents broke up a few months later.

As Ms. Steinberg headed back up the road to resume her responsibilities, the “Spamalot” actors were still immersed in their scene. Their show will be performed on the very last night of the session, after dark, the better to display the almost Broadway-caliber lighting design. After the actors have taken their final bows, a different kind of drama will ensue: the epic goodbyes, parents waiting in the wings, just before the drive home.