In the hope that you'll be able to do the right thing for yourself and your child, I am going to copy mermaid33's awesome and articulate advice to a woman in a difficult situation on a thread last week called 'I just can't get over it " or something like. Take the advice that applies....
So, what is it that you want? Do you want advice on how to get over it? There is no way to get over it because it's never going to go away and it's never going to change. The only thing that will change in this situation is you.
I'd like to say I feel sorry for you but you do enough of that on your own. Someone needs to give you a good swift kick in the butt and get you in gear because you have bigger problems than your cheating alcoholic boyfriend and how to keep him away from his other girlfriend and their kid. You are the head of your family, not your boyfriend, and the sooner you start accepting responsibility for that, both emotionally and financially, the better off you and your kids will be.
His other girlfriend doesn't want him in "her" baby's life because she doesn't want this alcoholic loser around her vulnerable infant. She's not doing anything about support right now because she knows when she does, the court will order that the baby have visitation with your boyfriend (and she knows he'll bring the baby around you.) This attitude of hers will last just about until the child is in school and starts needing things like school clothes and supplies and a fatherly presence because the kid's getting hard to handle on her own. Then she'll contact your boyfriend for child support. This, I guarantee. In fact, I double dog guarantee it.
The only glimmer of hope I see in your situation is that you have not married this man. Do not, under any circumstances, marry him. And he will ask you, the minute you start showing any independence (which I'll get to in a minute). As a single parent, you have access to many more government programs that can help you and your kids. Marrying this man will do nothing to change him (if kids didn't change him, do you think a ring will?) and you'll only saddle yourself with all of his debts and legal problems. As it stands, your boyfriend (he's not your husband) is legally and financially responsible for at least 4 children that you know of and god knows what else. Thank your lucky stars you don't have a divorce to have to go through on top of everything else; keep it that way.
My advice to you? If you spent just a fraction of the time you spend worrying about him and what he wants and what you can do to keep him from cheating on you again and instead focused on yourself and bettering your situation, you'd be a hell of a lot better off and so would your kids. All I read in your post is about him and what he's done and what he wants and what he might do in the future. I didn't hear one word about what you want out of life. Have you even asked yourself that? Am I the first person who has ever asked you that?
Do you have your high school diploma? If not, go get your GED. Do you need financial help? Look in the phone book for the right agencies to help you. Do you need legal help? I would strongly recommend contacting your nearest Legal Aid office - they will help you for free if you qualify, and it sounds like you do. The point is, you need to start doing something, anything, to pull yourself out of this hole you've dug for yourself. He is not the key to your happiness but if you don't do something pretty soon, he will be the cause of your downfall and the ruination of your children.
Start with the goal of doing one thing per day to change your situation. Make one phone call to someone who might help you. Blondie was right, start with Al-Anon; it's free! The people there have been through everything, and I can't guarantee you they'll be your personal therapists, but if you invest some time with this group (to better learn to cope with your situation - see, a step in the right direction!) I'm sure they'll have some leads on resources that can help you with your other problems.
After you've made one phone call, make another. And another. Contact your women's domestic violence program, it's in the phone book under "domestic violence". (They can help with emotional stuff, not just hitting.) If you are feeling depressed and can't afford a doctor, contact your county mental health department; they will help you get free medication. If you have a local community college, contact them. Just go up there and start talking to someone, anyone. They'll steer you in the right direction of who can really help you and they have programs for single moms to help them learn job skills to help their families. All of them offer help with financial aid (which you qualify for as a single parent - don't get married!) and some offer help with childcare and even transportation. Go to your local unemployment office; they have programs to help stay-at-homes get training to reenter the workforce. Look into AFDC or food programs (again, stay single!) If you go to church, talk to the people there; most churches have outreach programs. If someone says they can't help you, ask them if they know who can and don't stop. You have to make your problems known for people to help you.
I know it sounds scary; and it is. I know it sounds hard; and it is. But you're scared right now, aren't you? So what's the difference? If you sit there another year, two years, three years, four, five years, you're just going to find yourself five years older with five years fewer job skills and five years fewer options open to you. I know you wake up in the middle of the night worrying about him and worrying about paying the bills. If you're going to worry anyway, it's time to worry about yourself.
I don't mean to frighten you, but I would seriously consider contacting someone about filing for custody of your children. Call Legal Aid (or just call any and every attorney's office in your phone book and ask them if they know where you can get an attorney that does "pro bono" work (that means free of charge). A paralegal (in the phone book) can help you do the paperwork yourself for a small fee. Don't stop calling until you get an answer. I have seen women in your situation before and when men think they are losing their grip on their woman, they often resort to the one thing they know will really hurt you - the kids. Right now, he could take those kids from you in retaliation and disappear and there's not a damn thing you or the police can do about it. File for custody and child support so his wages get garnished and you get the support your kids deserve. You will need to consider making him leave the house again before this turns ugly. I have yet to see a man who drank not turn ugly when his life as he knows it is threatened so please be careful. You got him to leave once; do it again and then start legal proceedings. Get your ducks lined up beforehand so you have his financial help for as long as possible before you cut him off. I know that sounds harsh but this is the safety and welfare of your kids we're talking about. You have a duty to help them, not him.
I know it's easier to stay where you're at in life and tell yourself you're doing the right thing by keeping your family together and staying home and taking care of the kids but I promise you that this is going to be your downfall. There is no way you are going to prevent your boyfriend from drinking or leaving or cheating on you if he really wants to and maybe getting someone else pregnant so now his support order will be divided up 5 ways instead of 4. Or 6 or 7, depending on what he does. Please, I beg of you, for the sake of your three children, you have to be strong, stronger than you think you can be, stronger than you feel right now. You have to be brave and put yourself out there and give them an example to be proud of. Do not be embarrassed to ask for help. And keep asking until someone helps you; it will happen if you make it happen.
Despite what you think about it being a good thing that you're all back together, your kids will not thank you in the long run. All they are learning from this is that it's okay to be an alcoholic that abandons his duties and women let men come back into their lives and their beds after they've started another family with someone else and lied about it the whole time. I'm not trying to put you down here because lord knows I'm far from perfect myself. What I am trying to do is give you a wake up call on this gentle board here before life gives you a wake up call that's not so gentle.
Take steps to better yourself while it is still an option for you and not a necessity so your kids don't starve on the street.
Best of luck to you and the little ones. I really mean that. You can do this, I know you can. Your post doesn't indicate a stupid person, just stupid choices with this man. Trust me on this, I have been helping women in your situation turn things around for themselves for nearly 20 years. There is something bigger and better out there for you, there truly is. You deserve more than a man who drinks and cheats on you and holds you emotionally hostage. You take a few baby steps and see how things start changing and someday you'll look back and wonder how and why you ever put up with this crap. Honest.
(You know something, I almost thought about deleting this whole post because I know you'll be offended and I don't want to add to your hurt but I'm going to leave it in case it does someone else some good.)