Mr. Traoré never met his daughter, Djenebou, a quiet 17-year-old who now looks after her brothers as something of a surrogate parent. Unable to move to the United States with her mother, she grew up with relatives in Ivory Coast, and came to New York in 2002 after receiving “humanitarian parole.”

Their home, a jumble of New York and Africa, is filled with the laugh track of Disney Channel sitcoms and the smell of peanut stew. A pile of shoes lies by the door  leopard-print Timberland boots, shiny high-top sneakers, slippers, sandals and high heels.

Mrs. Traoré keeps hand-drawn Mother’s Day cards taped to her bedroom door and posters of Mecca taped to the living room walls. Those walls could use a fresh coat of paint, and the ragged carpet has seen better days. But the family is busy, and the house is well loved, a refuge from the rough streets of Hunts Point outside.

Mrs. Traoré is strict  she keeps her children indoors or in their small backyard  and she tries to limit television to an hour a day. Djenebou spends much of her time checking Facebook and juggling instant messages, but her sessions are routinely interrupted by the call to prayer, which Mrs. Traoré has set to issue from the family laptop’s speakers.

Mrs. Traoré wants her children to pray, but that can take some nudging. They pray together in her bedroom, and they have long, quiet conversations about their religion. And on Fridays, they visit a ground-floor mosque nearby on Southern Boulevard that sits opposite a graffiti-covered junkyard, down the street from El Mundo Department Store.

“I tell them we have to believe in God, you have to pray,” she said.

While she finishes her overnight shift at the hospital, the children get themselves up and prepare their bowls of cereal. She calls when she is five minutes away so they can jump in the car and race to school. “We’re always late,” she said. “Always, always.”

She sleeps until 3 p.m., and then picks them up from after-school programs, prepares dinner, reviews homework and checks backpacks before leaving for another night shift.