Depression Support Group
Depression is a real and debilitating condition that is often misunderstood by family and friends. Its meaning can range from a prolonged period of sadness to an actual mental illness with specific symptoms. Find and share experiences with others who are going through the same struggles.

You might want to just drop the whole custody issue (for fear of being denied any access by the courts) and leave it till you have been through some kind of rehabilitation.
I think you need to book yourself into some kind of hospital. You need to work on you before you try to raise two (perhaps three) children on your own. You will do them harm in your current state.
Your kids will still be there when you have sorted your life out. As to the pregnancy, you need to work out if you can look after another child right now, solo, with your current issues.
I seriously recommend booking yourself into a facility as fast as you possibly can, because the sooner you go in, the sooner you come out, and the less time is wasted before you can start making some serious choices about your life going forward.
There's no such thing as the 'perfect victim' in domestic violence situations. Victims aren't perfect housewives who cower in the corner. Most women yell and shout and fight back. But as I said... I don't know the situation and perhaps I'm ascribing things to it. Either way it sounds toxic and you were right to leave.
I don't know what to say about your children but I understand how alone you must feel. Just please make sure this current relationship isn't toxic or abusive... it's really easy to escape one and end up in another. I ended up with my own abuser after escaping my step dad, because for a while he at least seemed better than what I was used to - so I put up with things I shouldn't have put up with.
Take care of yourself.
From all that you have said it sounds like you have some nasty monkeys on your back that need to be resolved. Stopping the drink is one of the hardest and if you can keep sober that's fantastic!! Now going from a bad relationship straight into another that in itself has issues is not what I would call a good move. Instead of focussing on your love life you really should put all your energy into building bridges to your babies. Again being my opinion you only thoughts should be them. You need to focus on getting yourself into a healthy state physically and show these child services that you are more than competent to raise your children...try for joint custody. How is your relationship with your children? If its a close relationship then they can call you to arrange to meet you out front so you don't have to face your ex. The only people in your life right now should be you and your babies. If you can lower the tension with your first relationship and be able to be with your kids on a regular basis this will help ease the pain and symptoms of depression. Im in no way calling you a bad person or mother I would never judge another God knows Im far from perfect myself!! You sound like a very caring person who loves her children. I hope that you get some peace soon and I hope I haven't offended you.. best of luck.