Startingover2 always always always remember the very definition of an alcoholic is someone who will drink at the absolute wrong times, will drink when they promise not to drink, will drink because they won the lottery, will drink because they lost the lottery etc.
So YES fight for sole custody of DD and supervised visitation for him. It'll be worth the fight, if he puts up a fight.
It's great you didn't say anything about his drinking, you can tell by his actions he would just use it as one more opportunity to quack.
stay strong...it is so sad, no question, but there it is.
(((((hugs)))))
b