This is short term. Remember that. In the not too distant future there will be a schedule where he has to pick up the kids, or you drop them off at his place.
I wouldn't do anything about it until you reach that point. You can't force him to do anything anyway, and anything you do will come across as controlling...in the way he'll perceive it you'd be 'using the kids to control him'. Don't do it.
I put up with $hit for 18 months. And it will be another 6 months before it shifts. I mean, less time with kids, small cramped apartment, working crazy hours...WW isn't working, has the kids more, living in the same house...it wasn't fair, but it wouldn't have been right to force things out of turn. Instead I kept doing what was right, kept paying what was more than fair for CS, allowed her to take her own journey even if that meant partying and having a series of affairs...in the end things are shifting, we will be going to 50/50 soon, the CS will be dropping, I will be getting a bigger place in the summer...she might lose the house, I have no clue, but $hit's about to get real for her...she'll manage though, somehow. My point is I didn't have to force that. Don't try to solve problems that a little patience will solve for you.
Me:38 XW:38 T:11 years M:8 years Kids: S14, D11, D7 BD/Move out day: 6/17/14, D final Dec 15