The only thing that changed is that the parents have to go home while the kids are placed with sponsors rather than amnesty/refugee status for all.
There is a single act that puts the "breaking up the family" option into the realm of possibility and it is, illegal border crossing with your family. I get why they take the risk, but this isn't FDR 1942 either. The kids are now and will be fine, quite possibly better off in some cases.