The founder of Southwest Key made millions from housing migrant children. His nonprofit has stockpiled taxpayer dollars and possibly engaged in self-dealing with top executives.

Juan Sanchez grew up along the Mexican border in a two-bedroom house so crowded with children that he didn’t have a bed. But he fought his way to another life. He earned three degrees, including a doctorate in education from Harvard, before starting a nonprofit in his Texas hometown.

Mr. Sanchez has built an empire on the back of a crisis. His organization, Southwest Key Programs, now houses more migrant children than any other in the nation. Casting himself as a social-justice warrior, he calls himself El Presidente, a title inscribed outside his office and on the government contracts that helped make him rich.