This really isn't a GOP vs. Dem issue. The principle is a simple one of ethical treatment of others. If you are going to arrest parents trying to get into the country with their kids who are not otherwise in some sort of jeopardy (e.g. - abuse, being subjected to traffic, etc), find a way to hold the entire family together. Pointing out who was in control of what and when and what policy was at X time vs. Y time is pointless and dumb. We are in the here and now.
The admin is absolutely within the law to take a zero tolerance policy on illegal immigration. You can argue whether that should be their stance, but it is a rational position to take relative to the law. Crap, Canada does not generally accept asylum seekers coming into the country from the U.S. and Mexico isn't taking these immigrants on the same basis. But that isn't the point.
The point is no matter how you enforce against illegal immigration don't separate kids from their families. Putting that into practice no doubt comes with complications case to case. But for craps sake, that's the guiding and over arching principle. And the fact this admin didn't think that through when altering how they enforce the law was a total fucking miss. The fact they are deflecting blame for that huge miss onto others is bush league.