There is an important legal distinction which determines whether or not you're arrested and separated from your family: asylum seeker vs criminal migrant.

If you walk up to the border patrol checkpoint and request asylum you will not be separated from your family. Once we make sure you're not a known criminal we basically let you go and put you in the queue for the asylum process.

Conversely, if you attempt to cross the border between checkpoints you are generally an economically motivated undocumented migrant. In this case, if we catch you the first time we'll essentially let you go home with a warning. The second time you do this it's a felony and you go down the felony/criminal process path. If you go down that path you are under arrest, and if you're under arrest in the United States we don't put your kids in jail with you. Children are remanded to the HHS who will either place the children with extended family, in foster care, or other things like that.

So what happened and what's changed? If you're an economically motivated migrant the best outcome is you scoot across the border undetected. The second best outcome is you get asylum status (has restrictions like you can't work). The worst outcome is you go to jail. People began gaming the system, attempting to cross the border illegally and when caught would claim to be asylum seekers. The policy difference between Obama and Trump is that Obama's administration was basically more likely to let you get away with going on the asylum track even if you'd tried to cross the border illegally.

So as it stands today ICE (if Trump ordered it) could go back to the Obama policy of granting people who cross illegally and then claim asylum status only after they've been caught. This would greatly increase the number of people on the asylum track (no separation) and decrease the number of people on the criminal track (separation). Or I guess technically Trump could order ICE not arrest anyone crossing the border illegally. You give them a court date, release them to the public, and hope they show up. The concern here is the incentives. However, without a change to the law, ICE has no choice but to separate the families when you get arrested.

The case law in question is the 1997 Flores settlement, a class action lawsuit which resulted in essentially saying ICE had to release the children since they are not being charged with a crime.

If they want to enforce the border they will need to put in place a less inhuman/bad looking system. In the past presumably the way round this was to not enforce the legislation - let people in?