My ex made all kinds of blustering threats about how he would destroy me as a parent in court, get full custody of Kid, etc etc. Didn't happen. Your AH is NOT going to get sole custody of the kids with his record. The best outcome would probably be kids living with you and seeing him in small and controlled doses - this may preserve their relationship with their father better than being exposed to full-on alcoholic craziness, which is only going to increase as he gets sicker. Living with you, they have a chance at seeing him only when he's at his best.
My ex made a lot of noise about how Kid was the most important thing in his life and he would do anything for her and so forth, but when he's drinking, he loses interest in seeing her (he's seen her once, for two hours, in the last two weeks, and he lives less than ten minutes from me). I think he discovered that he can do a lot more drinking if he doesn't have to act sober because his child is around (although he still texts her about what a terrible person I am). From talking to other parents, I understand this is not an uncommon problem -
kids are an encumbrance when what you really want to do is drink. So your AH going on about his devotion to the kids may not last, unfortunately.