Parenting is very challenging and can be a trigger for sure. The very thing that is destroying your child is what you crave. A conundrum.
Not knowing any of your circumstances, where the other parent lives, what the custody arrangements are etc its hard to say what should be done. But based on your posts maybe letting your child go into a more stable, safe and predictable environment is best for both of you. Gives you the opportunity to care for you, keeps them from the emotional damage caused by active alcoholism. If he is asking to leave, that should be highly considered, assuming the other parent isn't more unstable.
There is no doubt that active alcoholism rips our kids apart. And early recovery can be equally as stressful for them because often we are stressed and irritable. So its a lose lose. And I believe its hard to even see the long term effects we have on our children until years of sobriety have passed. The kids often think, hey they quit drinking all will be well, and that often isn't the case. Both the alcoholic parent and the kid become so focused on the drinking that all other problems become minimal by comparison. Remove the alcohol and all the real issues start to come out. Plus dealing with a child that hasn't developed properly because of our own dysfunction. Very tough.
Do what is right for your child. And there is no solution in a bottle. Period. Until you fully accept that you will continue to hurt your child, often irreparably. That is a grim reality but one that needs to be faced in order to mitigate damage. I had a long conversation with my daughter last night, a lot of it about my drinking. I've been sober for quite a while now and she's really just facing her feelings. She had to repress things for so long just to survive. And I have had many periods of pretty long abstinence. I still caused awful emotional pain. Its hard to face, and even harder to listen to, but its important for both of us.