Sounds like his mom knows what she's talking about. Enabling prevents addicts from getting better, so unfortunately, protecting your boyfriend from the consequences of his actions is only going to make things worse for all of you - you, your babies and your boyfriend.
I wouldn't worry too much about what your boyfriend will do if you decide not to put up with the drug abuse in your home anymore. He is a grown man and addicts are extremely resourceful. When you quit being his enabler, he'll manage his life however he chooses. He may even seek help for his addiction. Or he may not. Again, you have no control over his choices. Until he wants to get better more than he wants to keep using, he's going to keep using.
Your children are just tiny and deserve all your attention right now. You have a choice regarding how you live your life but your babies don't. I'm glad you have your mom there to help since people who are high on xanax don't make very good childcare providers. And living with resentment and anger can really sap a mother's energy.
Keep reading and posting. It may help you find the strength and courage to deal with your situation.
You may want to check out a book called "Co-dependent no more" by Melanie Beatty. It has a lot of good information. Also, Alanon meetings can be helpful as well.