Paul Barreto moved into Room 2565 at the New Yorker Hotel the year after his father, Mickey Barreto, did. It was 2019 and the 135-square-foot queen-bed room in Midtown Manhattan felt like it could be a good home, or at least a better one.

It was nothing like where Paul, then 13, had most recently been living with his mother in California: There were no mice running around, no one was fighting outside his window and no strangers were stopping by at odd hours. At the hotel, Paul had the bed to himself, while his father slept on the floor with his boyfriend, Matthew Hannan.

And at last, Paul was back in school every day. Mr. Barreto had begun home-schooling Paul and his older brother, Jason, when Paul was in the third grade. But the boys did not have a curriculum to follow. Most days, Paul said, he watched hours of YouTube videos.

For the first time, Paul was making friends at school and socializing with them after class, something his parents had not allowed him to do.

Soon, though, things would unravel as they always did with his father, a delusional man with a short fuse, an obsession with conspiracy theories and a fondness for outlandish claims, like being the owner of Brazil. Over the years, Paul had learned how to avoid his father’s ire and ignore his ramblings. But now, in the cramped hotel room, he felt trapped.

Before Paul moved in, his father had already started a legal war with the hotel’s owners. First, Mr. Barreto took them to housing court and argued that an obscure New York City rent law could make Room 2565 his permanent residence. He won.