Ms. Rodríguez expected that Gerson would be held by the Border Patrol for a few days and then transferred to a government shelter for migrant children, from which her brother in Houston would eventually be able to claim him.

But Gerson seemed to disappear on the other side of the river.

For six frantic days, she heard nothing about her son — no word that he had been taken into custody, no contact with the uncle in Houston.