StongEnuf...he's just white knuckling it because he's afraid of losing his main enabler: you. Before long, without a recovery plan in place, he will drink again.
Seeing as your landlord is a good friend of the family, would it be possible to talk to him and see what can be done about reassigning the lease to your name only? I did the same when I left my AH; we re-assigned the lease and utilities to him only, and I left with my DD.
Again, this is something the social worker and a lawyer/legal aid can help you with. You need to know the legalities about throwing him out, especially once he starts drinking again. Seeing as the social worker is already aware that he's got a drinking problem and WANTs you to kick him out should he start again, the solution seems obvious: wait till he starts drinking again, even a beer at dinner, and call her. Ask her to help you get the ball rolling.
This way, the kids get to remain in the family home.