Hi, Jenn,
Wow, you have a lot on your plate right now. If your husband is an alcoholic, he most likely CAN'T refrain from drinking so he's in condition to drive. It certainly doesn't seem like a good idea to count on his getting you to the hospital--in fact, you should consider just planning on getting there some other way--a cab, a friend, an ambulance if necessary.
Sorry you're having to deal with this right now. Once the baby is born, I hope you will be able to make some Al-Anon meetings. I have a feeling you are going to need them.