Ugh. It's so difficult in this position. Unless your ex's boyfriend has drunk driving convictions against him, I'm not sure how you go about protecting your kids. Does your son have a cell phone? If so, you could have a discussion with him about how he can always call you instead of getting in the car with BF if he seems drunk.Or maybe, just ask son whether he ever feels uncomfortable with BF driving?
The good news is, hopefully, this guy will not last long. He'll cheat on your exW too. In fact, maybe this is why your ex is so bent out of shape about you moving on - maybe she has started to realize that the grass wasn't greener with this guy.