Effect. I could be wrong though, but he's alluded to her not being in a good enough place to see the kids and it wasn't just about Drew.
As for the prison visit stuff, it made no sense. But thats the writing on this show. Maybe he doesn't mind them visiting her in prison because she's contained? Remember when he agreed to have her see them a few months ago, it had to be supervised. He didn't trust her, given what she did with Daisy. My guess is he thought she'd flee with the kids and Drew, but thats just a guess.