Three shots of hard liquor, taken with dinner. Yes, this is a guy with a substantial alcohol problem. Yes, you should be worried. He's not "battling alcoholism;" he is succumbing to alcoholism. There will be a price for that. If you stay in a relationship with him, you too will pay a high price. That's how alcolholism works.

He may well be "really nice." All kinds of people engage in alcohol abuse. Unfortunately, those who do so chronically end up neglecting their responsibilities because of their involvement with liquor. He's already neglecting his relationship with his kids. If he doesn't prioritize his own children, he's not going to prioritize you. This will hurt you, and it's inevitable. His wife probably had some good reasons for ending her marriage.

You can't help someone else reach a goal that they haven't selected for themselves. I am with a man who drank heavily for the first 12 years of our relationship. We are both still paying for that, although he has not been drunk for twenty years. I don't recommend taking on this burden.