The big crisis under Obama was unaccompanied minors. The administration didn't handle it perfectly, but it was clear that they were trying to figure out the best way to deal with a very difficult situation. (They couldn't just let them go, as they were minors, nor could they necessarily send them back.)
They did not engage in mass family separation. The only times children were taken from adults were under very specific, exceptional circumstances where the children were somehow in particular danger of physical or sexual abuse (or signs of trafficking).
Crossing the border is a misdemeanor. For most of Obama's term, this was treated as suchlike public intoxication, or vandalism, or some traffic tickets. You don't get your kids taken away for thathell, you rarely go to jail for that--and as such separations weren't enforced (again, unless there was a compelling reason why).
The Trump/Sessions regime has decided to essentially imprison all these people pending trials. They scrapped a pilot program that had a 99.6% effective return rate for those awaiting trial, because it wasn't punitive enough. They said out loud that they wanted family separations to be a deterrent. They said this months ago. Any pretending otherwiseincluding by SHSis a lie. And it's fucking disgraceful.
There have been so many attempts to fix some of the broken parts of the American immigration system, including a bill under Obama that passed the Senate with 60 votes and would have passed the Housebut the obstructionist wing of the Republican party refused the vote. As others have said, they don't want to solve the problem, they want the issue because it gins up their base and helps keep them in power. And because people like Stephen Miller*, who is an avowed nationalist and an anti-immigrant piece of work, is in charge of immigration policy.
It's all fucking disgusting.
If you don't know about him, you should read this amazing* interview in the New York Times NYT. It includes the ridiculous anecdote of the time Miller "jumped, uninvited, into the final stretch of a girls’ track meet, apparently intent on proving his athletic supremacy over the opposite sex. The fact that this guy is in power is terrifying.