The parents are free to take their children and either enter the United States legally at a border crossing (if their papers are in order), or return home. No one is making them cross in the middle of a wilderness, knowing it is illegal. None of them are fleeing anything so horrible that they would qualify for asylum.
Trump has asked permission to keep the parents and children together while they are being held pending a decision on deporting them, but Congress needs to pass a statute to allow it.