There seems to be an obvious easy solution to this: a way to maintain the border without ripping kids away from their parents. You mentioned it and then seemed to forget it. The idea is to incarcerate parents together with their children until their cases are heard. They can then be deported together. Of course a process is needed to first determine if the adults are truly the parents of the children with them, but all this seems workable.
Strict but humane enforcement of our immigration laws is what we should be aiming for.