I recommend talking to your AH. You should find a time when your AH is sober and you are calm to talk about what you said here. Your AH can't read your mind and it's not fair to make him guess. He may know you are upset, but unless you tell him WHY, he won't know.
p.s. It doesn't sound like it's very fun playing board games with a drunk. Next time, you should consider saying no. You may also want to consider saying no the next time he asks you to go to the LQ store - you don't need to support his drinking by going with him to the store that fuels his addiction. I know you are doing the best you can & you deserve a lot of credit for that, but setting boundaries that protect you and your children and do not support his drinking will help you immensely. Hang in there and good luck!