What if it became an order to deport all illegal alien parents of children born here? The parents would have a choice to either take the child with them or leave them behind. And if left behind, the child would have to go to a child welfare unit, or to a family of legal residents. Nothing would be said about the anchor babies having to leave the country. It would be their parents that would have to leave.
It should be referred to as “family unification” (in the parents’ legal country of residence). After all, who can be opposed to family unification?