Suggestion (although I hesitate to make one)
How about this: Find yourself a good counselor (I would suggest a psychologist who has a background in addiction counseling) and go speak with him or her about your dilemma? If you cannot afford that, how about Al-Anon meetings? If you don't have meetings you can get the Al-Anon "Big Book" (similar to AA's Big Book). I would also suggest you go to AA meetings to get the feel and "flavor" for how alcoholics in recovery deal with their addiction. Generally, they're more than glad to give you a free copy of their Big Book - lots of great knowledge and insight in that book! It's about a lot more than the stories in the second part of the book about alcoholics and their story that led them to recovery.
Educate yourself. Learn and read as much as you can. We have online meetings here on a weekly basis. They're very helpful. Find people who have a healthy perspective on life - friends, family, new friends you can make, co-workers. Don't have a bitch session with them about your problems, but look to them for support and strength.
You realize your problem. You're just stuck in a spot where you don't know what to do. Only you can make that decision. Think about your children, think about your peace of mind, and consider this: if you left and got an apartment you would be financially strapped. There IS financial aid out there for women in your position. If not, you could still survive - and even thrive - in a living situation that is better than what you have now.
Nobody knows what the future holds, but if you work on healing yourself, you will naturally become involved with healthier people. Who's to say somewhere up the road you might meet a man who wants to be a real father to your children and a real partner for you????