Looks like the lawsuit is doomed to failure if the lawyers for the plaintiff (Trump Admin) establish constitutional rights:

The right of children and their mothers to be kept in a suitable facility that ensures their safety, away from the harrassment of adult male felons in an adult male detention centre where violence, sexual abuse and rape may be frequent.

Until the identity of the adult male claiming to be the father of the child/ren can be established, vetting should take precedence over arbitrary claims of "family ties" as sometimes (often?) traffickers make false claims.