I think you should get yourself and your kids out of this situation. You asked for something reasonable, that he pursue treatment and you know that this cycle is going to come around again if he doesn't.

In the big picture children need to see their parents making healthy decisions for themselves. Right now they have a front row seat to the decisions he is making and you have an opportunity to model the kind of choice you would want them to make for themselves if they were in your situation.

Kids can find fault in ANYTHING you do, then they can use it to hurt you because it's just what they do. It's how they test boundaries and how they figure out the world. But if one of them was in your relationship you would want them to be safe.

It really sounds like right now they only have one parent who can consistently protect them and they need to be protected.