Vilma Carrillo was one of a group of migrant women flown to Texas in July from a detention center in Georgia to be reunited with their children, who had been separated from them as part of the Trump administration’s clampdown at the border.

Over the next several days, she watched as immigration officials paged one mother after another and took them to meet their children.

“I was never called,” Ms. Carrillo said.

Her heart in tatters, the 38-year-old Guatemalan woman was sent back to the Georgia detention center without her daughter, Yeisvi, 11. “The others got their children back,” she said, “I was left with my despair.” She hasn’t seen her daughter since they were separated in May, but they talk on the phone twice a week.

Ms. Carrillo has been caught at the intersection of several Trump administration policies intended to make it harder for Central American migrants to settle in the United States. Her case is more serious than what thousands of other migrant families have faced: Because her daughter is an American citizen, Ms. Carrillo has been told that she could lose custody.