Mr. Miranda, the Homeland Security spokesman, said that there had been no deliberate separation of families, but that there might have been instances where adult family members could not legally be processed or detained together and became separated.

“In cases where that has happened and we become aware of the issue, we take proactive steps to bring such family members back together,” he said in a statement.

Staff members from Kids in Need of Defense, the advocacy group, said some Venezuelans now stranded in Mexico were so desperate that they were trying to send their children alone to safety in the United States, knowing that minors would not be expelled — a situation that creates additional separations.

“We have counseled them on the risks associated with taking this action,” said Megan McKenna, the group’s senior director of public engagement.

Mr. Peñaranda, a car detailer, and his wife, a schoolteacher, said they decided to travel to the United States after their family was denied asylum in Costa Rica, where they had spent six years, among millions of Venezuelans who have sought refuge in neighboring countries.

After crossing the border in El Paso on Oct. 6, Mr. Peñaranda said he and his stepson spent several days in a frigid room and then were handcuffed, shackled and shuffled up the stairs of a plane that flew them to Brownsville, Texas, a border town where they were finally released.

“We thought we would all be together soon,” Mr. Peñaranda said.

Ms. Yepez and her daughter were flown to Laredo, Texas, more than 200 miles from Brownsville, where they were among more than 100 migrants who shared a fetid warehouse, she recalled.