A career official at the civil rights office of the Homeland Security Department, whose job is to process complaints by people who feel they have been mistreated, watched members of his team crumple into tears at their desks. They were overwhelmed with hundreds of pleas a week, written on behalf of migrant parents and children searching desperately for one another. The pleas came with photographs taken at the border of the missing children. They showed “5-year-olds who don’t know how to take a picture without smiling,” said the official, who spoke on the condition of anonymity. “They look like school photos.”

A manager in the same department printed some of the photographs in an attempt to seek support, both logistical and emotional, from Cameron Quinn, who was appointed by President Trump to oversee their work, the official said. The manager presented Ms. Quinn with the children’s photos at a meeting.

Interviews with more than a dozen employees at the three federal agencies tasked with carrying out the president’s orders said they were feeling alienated and exhausted after being ordered to carry out, then halt, the separations — as well as deal with the fallout.