Of most concern to me is your second sentence where you say your husband’s drinking issues have been “addressed”. Sadly, they have not. Your husband is buying your tolerance by managing his drinking most of the time. But he has a long way to go before he is sober and adult in his thinking and behavior.
He may be trying to have the father he never had by spending time with his dad now. But instead of joining his dad in the drinking, he should be insisting that his dad join him in sobriety. Your husband may believe that the only way to have his father in his life is to accept his dad’s terms, but the price is very high for doing so.
You are early in your marriage. You do need quality time together. The 5-year-old needs his dad to be an adult, not a “son” to his own father.
If this marriage is to last, your husband must acknowledge that he continues to be a barely-controlled alcoholic. He needs to get seriously involved with substance abuse treatment. It is not unusual for someone with a history of alcohol abuse to be inconsistent in his ability to make good decisions. This is one of the issues that would be addressed in treatment.
Further, I suggest that you get involved with Al-Anon, an organization that supports people who love people who have a problem with alcohol.
I also suggest couples therapy to deal with your husband’s unresolved issues with his father and how they are impacting your marriage and his parenting of his own son. He should not be spending any time with his father that involves drinking. His priority should be on making a happy and functional family with you and his son. If he won’t, you have some very difficult decisions to make.
I wish you well.