To me this is quite a significant alcohol problem. I'm not an expert by any means but have read a lot of books about alcohol and addiction in general. The reason I am saying this is a serious problem is not just because of the quantity or frequency of his drinking. It's because his addiction means that alcohol has become the focal point and crept it's way into every area of his life. Part of addiction is the fact that the addict continues with the behaviour dispite negative effects. This is affecting multiple relationships, parenting, socialising. It is also not the case that he just simply doesn't get that his drinking is not appropriate, or that it is a cultural thing. Yes I agree that alcohol is pervasive in society and socially acceptable to a degree, but that is just one thing which helps him stay in denial. That thing about the only thing that makes him happy is drinking - that is a big red flag. That is the neurobiological and psychological impact of alcoholism. It impacts your brain chemistry, and your reward centres. Basically, alcohol makes you feel good temporarily, then quickly the body responds to compensate which makes you feel worse. Ultimately he is drinking to relieve the negative impacts of having consumed alcohol. It's a cycle. That's part of what alcohol does, and why it is so addictive.
In my opinion, this isn't a reflection on you or your baby in any way. It's not that he can't ever find happiness and fulfilment in any other way, just not while he is psychologically dependant on alcohol. But in order to do that, he would need to confront his alcohol issue, get sober, and work to rebuild himself psychologically. At the moment he is basically at the total mercy of the biological effects of alcohol, and until he accepts that, it will remain the case.
The thing about alcohol and his bubble is very concerning. Someone said that in the end the addict finds himself alone in a room with a bottle, and no one left around him. Mentally he is already heading in that direction. In my opinion the choice for an addict is a) you can have the substance or b) you can have everything else in life. You can't have a and b. They can't coexist in the long-term. But it is for the addict to realise and accept this themselves, confront this. That needs to happen in order for change to occur. Some reach that point and overcome addiction, some do not.
The reason why I am saying that controlling his alcohol intake will not help is because the number of drinks he takes is only an outward symptom and effect of a deeper psychological and biological problem - his addiction to alcohol. Alcoholism isn't just about the amount you drink. It's about the impact drinking has and it's about continuing to do it when it is causing problems. Limiting his drinks will not solve that problem, it will just draw you into the drama and unhealthy psychological effects which alcoholism has on those around it. Lots of people call alcoholism the family disease. This is because of the serious impacts that living with an addict have on the psychology and wellbeing of others. We get drawn into roles and play a part in the addiction, partly due to the feeling that they can/should control or cause or change the addictive behavior. This leads to all kind of psychological distress and keeps us also locked into the addictive cycle. I am not great at explaining exactly how this happens, but I think the AlAnon website will probably have quite a lot of information and advice which explains this better than I could. They may also have online meetings.
The fact that he has lost relationships in the past due to drinking, has previously attended AA, and that his stepdad is recommended AlAnon are all big indications that this is a long-term problem. He is an addict who has returned to a state of denial. This was the case before you met. It will remain the case until he takes responsibility. That may never happen. And ultimately that is his journey.
As you mentioned, he has not listened to your boundaries about the level of drinking you are comfortable living with. He has probably taken the fact that you go up to listen to music as a sign that he can simply continue to drink and you will accept it. He is already on that path to bring the addict alone in the room with his bottle. Only he can make that choice between a) and b).
Which in my opinion leaves you with two choices about your own life and wellbeing. A) decide that you can live with his addiction and the fact that he may never come out of denial, and may continue to sink in to addiction - and accept that you can't influence this either way, or b) decide that you can't live with someone in active addiction and let him know he can clean up totally and get help, or leave.
The point of option b) isn't to shock him into sobriety. It is to set a strong boundary and make a choice about what you accept as your life and relationship. If he goes, he goes. If he stays and gets sober, great. Either way you are stepping off the 'merrygoround' of addiction.
I feel terrible for you as it must be awful going through this as a young baby. I just felt I needed to post, as from your OP I felt that there were a lot of red flags about how far his addiction has progressed psychologically. As you mentioned, it has gone so far as to impact his ability to be a good father, partner and family member. And still he persists and stays in denial. Only he can change that.