To be honest, if he has not complied to your needs in the past, the chance of it happening in the future are slim and none. There is more to addiction than just using. Behaviors continue, even when not using.
He has made it clear, he would rather be comfortable than do the right thing, let you and your son stay in the home.
As for him being guilty...he's playing you...more words that do not mean a thing...actions speak for themselves.
On top of all this, he is a cheater, a totally unrelated issue. I sure hope that you are going to meetings and working on you.
As for telling him he can live a healthy lifestyle with you if he chooses to this is just opening the door for more problems, let him prove himself, leave it at that. Of coarse, he will agree "That is what I want, a healthy lifestyle", more verbage that means nothing.
Where in all of this are your bounderies to protect you and your child?