MCALLEN, Texas (AP) — A mother cradled a crying toddler as she waited in line with 20 other women to shower. Dozens of fathers quietly held their children's hands in an enclosure made of chain-link fencing.

While these families were held at an overcrowded Border Patrol processing center, a fresh wave of migrants crossed the nearby river separating the U.S. and Mexico and waited for border agents to bring them to the same facility. One Honduran woman carried a feverish 7-month-old baby.

The cycle is repeated multiple times a day. Waves of desperate families are trying to cross the border almost...