So he's upset that he told his ex he's struggling with his alcoholism and she said this in court?! Am I getting it right?
What in God's name did he think she'd do with that info? Hug him and sing kumbaya?! Actually, given the "poor me" attitude that my own AH espouses maybe he really thought sharing that with her was a way to get pity and there'd be no impact for him related to his child...
I'm sorry you are having to deal with the fall out-- and I know that feeling so well of saying "oh why did I respond or engage in that at all" after the fact... You'll get "better" each time, I'm sure... If I can manage to be doing better (something I NEVER imagined), than anyone can! Seriously...