“On the other hand, many of them have children born here who are.”
Which means they get welfare legally.
“In addition there are people who cheat and tell the welfare folks they are American citizens.”
Just like e-verify they have to provide a social security number to get it.
I think all situations can be addressed equitably by simply shipping the parents back and adopting the children out, and then, if the parents try to come back into the United States, they get a bill for our trouble in adopting their kids out.
It wouldn't take more than half a dozen instances of that sort of treatment and they'd quit having kids here.