Every administration, to a growing degree, attempted to do things about the illegal immigration problem. If Obama wanted to do anything other than what he was actually able to do, McConnell and the Senate would block him. I don't know as much as I should about the particulars of Obama's border policy, but he didn't put kids in cages, separate them from their families, and make it impossible to reunite them. He promoted DACA, which is sane and makes sense.
Trump is merely behaving like a prick for the audience of his Base. They're behaving as if this is a "last stand for White People and Christians". They don't like the "writing on the wall" -- the inevitable demographic changes that lead to no single racial group remaining a majority.
I have an associate, a member of my 1965 high-school class, who recently made the remark that the influx of Latinos and Asians is overwhelming the White "majority". This -- from a guy who says he's not a racist, but he blames African-Americans for "ruining" his former Chicago neighborhood. Another fellow classmate wrote a novel, and he asked him if he could read it. The second classmate told him to contribute $20 to the Southern Poverty Law Center -- SPLC -- and he could have a copy of the novel. My . . . associate . . . . says "Why should I contribute to a cause or organization I don't believe in?"
Took a while for his remark to sink in. Who WOULD think that SPLC does things they don't agree with? Suing hate criminals? Who wouldn't agree with that?