My RXAH, left when I was 2weeks away from having our first child together. We both have children from previous relationships.
I immediately went into stress overload. Lost 16 pounds in 10 days, my BP shot through the roof and I could not sleep at all. My DR told me to knock it off or I could stroke out.
I went to my first AA meeting that night because Al-Anon is only once a week here, and I swear everyone at AA new I was a lost soul. They were so incredibly comforting to me.
Anyways, as to the birth of your child and what to do. I text and called my AH work and left messages everytime the date was changed for my scheduled C-section which was twice before I ever had our DD. The only response I got from him, is he would be there for her, not me.
Then, surprise, I had to have emergency C-section due to my BP, and the toll it was taking on our child. I too felt he really wasn't entitled to be there for her birth. HOWEVER, I made an attempt to call him at work. I called the office number. Nobody answered. Good Enough for me. I called my Mother and she came and went in with me.
The result of not making a big effort to contact him was this. He has HUGE and I mean HUGE resentments toward me for cutting him out of the birth. I didn't cut him out, I just didn't go over the top to try to get him chased down at work to be there. He was really pissed off at me.
We have a long story, but ultimately he went to rehab about 5-6 weeks after our daughter was born. He worked on himself. I worked on me. We are now very happy together, but on occasion it does still come up. He is hurt by my lack of action.
SOO, I would suggest this. If he isn't blasted out of his mind, don't cut him out of the birth. Try to have a back up plan, if you aren't able to reach him, or he isn't in a condition to be there. Maybe have a friend to be there, as well as him, and then if he isn't able then so be it.
Birthing your child is a life event. It is the beginning of so many things. He may well be an alcoholic, but that doesn't mean he will have any less love for your child. Maybe he will follow through this time on getting help and getting sober. Maybe not. Thats his decision.
Think long and hard about why you wouldn't want him there. Make sure that if you decide that he isn't to be there, they are really valid reasons, like he is drunk off his ass, or something like that.
Part of the reason I didn't make a big attempt to have my RAH chased down, is because I was pissed, I was hurt, I was "sick" if you will from all the codie crap, and I too was harboring big resentments toward him for leaving and choosing alcohol over me and our child. Don't do what I did. I don't have huge regrets over my decision, but there will come a day when our daughter asks him if he seen her be born, and I will have to answer that. ---Seriously I may have done everything possible to let him know and he may not have came, and then it would have been on him. As it is, I didn't do anything other than 1 phone call, so now it lies on me.
Hope that helps a little. Sorry your going through this.