Hi,
I went through something similar except I thankfully didn't have a child with the a$$hole.
My ex and I used to fight constantly about two things: my purportedly not loving him as much as he loved me, and his drinking and emotional abuse. He was a black hole of need and nothing could fill it.
He was "trying" (and failing) to get sober for three of the four years we were together. He finally ended up very depressed and threatening suicide. I couldn't handle the situation anymore so I contacted his brother whom I had never met before--I found his email address on Twitter. His brother had no idea whatsoever he was an alcoholic and confronted my ex about it. Within an hour of them talking, my exabf had written me a one paragraph email, blaming our relationship for his drinking, telling me our relationship was over, and wishing me a good life.
His brother who obviously knows nothing about alcoholism believed this BS. His brother told me "He drinks because he can't handle his emotions for you. If he quits you cold turkey, he will be able to quit alcohol cold turkey too." I wrote back and told his brother that my ex couldn't handle his emotions about anything, and that I hoped I was wrong but I did not believe this was a legitimate attempt at sobriety. Turns out I was right and my exabf is still drinking.
What I have learned on SR as it relates to situations like mine and yours is that an alcoholic does not want anyone in his life who gets in the way of his drinking. They look for enablers--people who often unknowingly support the drinking. As soon as you are not enabling him anymore and instead making it harder for him to drink, you need to go.
In my case, my ex was tired of feeling exposed by me. He couldn't hide his drinking anymore from me; I had all his little manipulations figured out. Then I crossed a big line bringing his brother into things. He felt backed into a corner and had to make a drastic move to be able to keep his real love, alcohol. He knew if his brother and I spent too much time talking about him, his brother would force him into some kind of treatment.
The way the two of them treated me at the end was really devastating. It was like I was some mistress with a dirty little secret who they needed to silence as soon as possible. I NEVER thought my ex could ever turn on me like he did. The way he claimed to love me made something like that seem almost incomprehensible. I deeply trusted that he'd always be in my life, at least in the capacity of a friend. People split up, that's normal, but to be disposed of like I was was something totally different.
Now I know that alcoholics are driven by need and aren't really capable of love. Your ex is just caught in the grips of the disease. For your child's sake, I hope he is really getting sober, but for some reason I doubt it.
Someday you are going to wake up and be thankful he is out of your life because you will have learned that there is no way to have a peaceful life living with an active A. Until then, we are here for you. We know how much it hurts!!