Personally, I would not put any effort into a relationship that has no chance of being healthy while he is a practicing alcoholic.
The idea that if you make the moves towards mending the relationship would help him to stop drinking or heal enough to be a safe partner is a fallacy.
I believe that while it might be true he works a stressful job and wants more appreciation, he is looking for external circumstances to dictate his moves. It’s just false. An alcoholic has an illness, an addiction and the idea it’s caused in any way because his family doesn’t appreciate him is a lack of accountability you just can’t work with.
I would tell him that you can see that what he does and what he wants is at odds with each other. Being a husband is more than just being a provider, it’s being a connected partner. This is not something he can offer so long as he won’t work on his issues. Right now, he has not only cheated but keeps putting the blame of his behaviors and their natural consequence at your feet.
I think attending some Al-anon meetings might help you with strategies, coping and where to firmly place accountability. Are you doing IC? Is he? This situation is not something you can change in your own by being more loving. I can appreciate your ability to self reflect, but sometimes self reflection might look more like this:
What do you want in life? What do you need to see happen? What is holding you back from making the best decisions for yourself? Are you prepared to offer tough love or remove yourself from the situation entirely?
Your husband can’t even start his journey to get his life straight until he puts down the alcohol. Until that time you need to think about putting your own oxygen mask and coming up with how you are going to move forward without seeing him make these much needed changes not just for his wife and child but for himself as well.
Personally if my husband were drunk and begging for affection, I don’t think that could be a bigger turn off. So why blame yourself for being turned off by what most anyone would be?