You really have a full plate and I can understand your fear and confusion.
How much help is your family willing to provide for you? Look at this realistically. I know that for myself, I could not depend on anyone in my family, so all my decisions were based on "Can I do this myself or do I need someone's help and where do I get that?"
If he truly is sincere in his efforts to get help and is a good provider and father, against my core beliefs, I'd go back after a little bit if the family help starts getting less dependable or relations get sticky. If he is willing to put in his time to help you then get it and possibly this issue will have to come back for answers a little later in time.
The first year of your life is going to be chaos with those twins and you'll need all the help you can get. I was a single parent and I am not going to be so rash or righteous as to tell you to do it yourself because you are a human, not a damn machine! A woman can only take so much!
If he is abusive, if his behavior impinges on the family finances, then that's another matter that you'll have to weigh in on. Possibly some help from the state might be where you'll have to look if family won't help out. For sure, if he's not living with you you have every right to have a temporary order for child support and maybe you could argue for a year's alimony as well. Afterall you put up with his behavior for years, nurtured him and now you bore his twins!
I will spare you a birth control lecture here, only to mention that even if you aren't seeing him or sleeping with anyone else you should be on something just in case he tempts you again. A woman can be imprisoned simply by biology if she's not careful.