I'd like to 'think' that I'd sober up quick and get into a recovery program if faced with being homeless,but that's just me. I also know that's not the case for lots of addicted people. We all have our own priorities. I really think you'll have to get the ball rolling on your separation/divorce because he doesn't seem ready to stop. As far as expensive lawyers, if there's no kids or joint assets it should be a relatively cheap process. I also doubt that he can afford an expensive divorce 'battle' if he can't afford his own place..
Also.. The friends and family section here might be able to give you some more advice on leaving the A.