If you have proof that he is an alcoholic, you can demand, through your custody and divorce proceedings that he abstain from consumming alcohol while caring for your son. Sure, this means you'll have to be the booze police for some time, but that specific provision is what put my XAH off from wanting to take DD for a long period of time, because he can't be without his booze. I made sure to indicate that if I at any time found him to be consumming alcohol while with DD, that I would request supervised visitation.
I SO know what dilemma you're facing, wondering if it would be any better to share custody with an irresponsible alcoholic rather than just "tough it out" with him. It's what kept me in my marriage longer than I should have stayed; I was terrified of the outcome. And yet, here I stand, 8 months later, with sole custody and my divorce in hand, and XAH is slowly disappearing. It shocks even me how HP has my back.
Remaining married to this man is really your decision alone, HOWEVER I would point out that by doing so, you're sending a message to your son that it is acceptable for a man behave the way your H is behaving (and that women will stand by while their spouse drinks away the marriage). Perhaps if you think of your son behaving like this father, it'll ellicit a different line of thought...Perhaps if you spoke with some ACOA you might understand what it's like to grow up in a household where there's a big elephant no one is allowed to speak of.
Yes, it's true that you'll still have to deal with your AH if you are divorced, but you will have some DISTANCE and SPACE from him.
Am I to understand that your child is of high school age? Then if that is the case, he's old enough to express to the courts where he wants to stay. The courts will take into account his opinion in the matter.
If he isn't that age, then there are ways to get around 50/50 custody.
I hope you don't see this as a flame. I just wanted to respond as someone who's BTDT and make it through ok.