I left my first husband when he had been sober for almost 15 years. It had nothing to do with his alcoholism, nor even any failings on his part as a husband. I simply felt empty in the relationship. It was me, not him.
We had two young boys (elementary school age), who stayed with him (because of work schedules, he'd always done more of the day-to-day parenting stuff, and he was frankly the better, more patient parent of the two of us).
After some initial hurt/anger on his part, we had a very amicable divorce and are good friends to this day. Our kids are in late 20s/early 30s. We all spend holidays together. They were not embittered by the divorce.
I'm not suggesting this is possible for everyone, but it is possible to divorce without having a "war" and without significant damage to kids.
You might want to re-think how you are framing this in your mind. You say she "hasn't been a good wife." Maybe she hasn't been a good wife, in part, because the relationship simply isn't right. Not that you just dismiss the alcoholism, but the bottom line is that you aren't happy in the relationship, which may not be anyone's "fault."
Have you talked to a lawyer about possible legal separation? That might give you both some space to work things out, one way or another. If not to continue the relationship, to determine how to work out a civilized divorce that is fair to both of you and to your child. If you approach this in a non-adversarial way, there may be hope for you both to have a good co-parenting relationship, which would be great for your child.