Maybe you leaving him/booting him out (er - the latter, please, you have kids) will turn out to be the huge wake-up slap that he's so far been missing? After all, if what blocks your relationship and progress path is a boulder (his) then prodding, punching or kicking it isn't going to work, is it - stands to reason. You need dynamite.
The kids fall out, sometimes permanently, with their schoolfriends. Use that as an analogy that they'll instantly grasp and understand. But remind them that all that will change for them will be that whenever they see daddy it'll be in his own place, and ensure that they know the decision to split was nothing to do with them or how they were or did, and solely and exclusively to do with your 'boyfriend-girlfriendship', and that their relationship with each of you will not only not change but will undoubtedly become BETTER. Remind them also (they are "me want" kids, after all) of the perks: TWO sets of pretty much everything, including houses.
If mum screams whenever she sees a spider, the kids tend to follow suit. Same principle applies here: if you're coping (which includes crying that you can get back off the floor from, with a 'haaah, that's better, I needed that [smile]') then they'll cope too.
Start collecting evidence of how hard his habit is and how incapable of functioning it makes him because, IF he fails to change his ways on cue, you won't want him having unsupervised visitation rights until he does.
Not sure what else you want to know at this point but - fire away! Alternatively, there are lots of expert How To books available from Amazon and the like (including 'It's Not Your Fault, Koko Bear'). And, WELL DONE for having the mettle to do the right thing.
Discussion closed - why not create your own thread?