Ms. Batista learned of possible deformities and other deficiencies that could develop after they were born. “The doctor said, ‘Your girls won’t be anything in this world,’” she recalled.

While her boyfriend was shocked by the diagnosis, Ms. Batista said he told her, “I want my daughters.” She said they felt pressure from doctors to abort the pregnancy but refused. “I was afraid that no one would love my kids,” she said, tearing up. But she decided that “I’m their mother, and as the girls grow up, I will give them all the love they need.”

The couple had met working at a packing company in New Jersey in 2011. He drove a bus for the factory, where she filled boxes with lotions and perfumes. What began as a casual flirtation became more serious when he met her challenge of finding them a place to live together. But the carefree part of their romance ended, Ms. Batista said, when they learned of the high-risk pregnancy. As the pregnancy progressed, she could no longer travel to care for her mother, who has since recovered and moved to New York. Ms. Batista said she grew lonely and depressed.