What do you mean when you say "on his way to sober" was he using and promising to stop or had he quit briefly?
I wish I had done a lot of things differently when I was pregnant by my alcoholic ex (our son is now 5 and my ex has almost no contact with him, he never sought any kind of recovery and is still active in his disease).
This may sound crazy, but one of the best things you can do right now is stop worrying about what your bf chooses to do. It won't help him and it will only cause you stress, which is hard on you and the baby.
Have you tried Naranon or Alanon meetings or sought any kind of support for yourself? That is the best thing to do, especially working through anger and resentment. I sure had a lot of that and Alanon has been a lifesaver.
Your bf is going to do what he is going to do, that's all outside your ability to control. What you can do is start making plans for yourself and your child that don't depend on him being sober. That's not something you can count on, I'm sorry to say.
I made the mistake of hanging my definitions of happiness and success on my ex quitting drinking so we could have a family, and that never happened. I would have been better off on my own without living through 5 years of his drunken craziness and lies and promises and abuse.