Or just start a rumor that the US is deporting all these children to China so they can be processed into pet food
Huge areas that are bordered on three sides with large, uncrossable fences -except for the south-facing side, which will be open to Old Meh-hi-co.
Once they are released into the area they can be told they have a choice. Stay there in the compound/"National Preserve Park" where they are welcome to forage for whatever they can find, or start walking back south.
With a suitable warning that anyone attempting to go over or around the miles-long fences and escape that way will be shot as terrorist invaders.
They should get the hint fairly quickly.