I also concur that at this time you might simply have to live with the status quo, much as you might wish the situation to be different than it is.
Your brother is not the problem. You still have a lot of work to do to get your life onto an even keel. As a parent, I would not expose children who have been through a lot of insecurity to anything that increases their sense of insecurity, and right now (especially with you still indulging in bad habits and justifying it) you are not going to increase their sense of calm and security. You need to demonstrate to your brother that you have a stable life, and all you're showing him is that you are still in denial.
Work with your counselor. The fact that you are (drinking) is not the problem, the problem is that you act like everything will be all right if you and your brother can just get together as friends. That glosses over that your behavior has caused a lot of damage. That is on you to fix, for your own sake. It is not your brother's problem. His problem is to make a good place for the kids.
Time will heal this, if you can create a better life for yourself. But I don't think there is a quick fix available that involves you and your brother singing Kumbaya. You still have to go through the grind of working on you. I'm sorry.
I'm sorry for all of your pain. Life sure an seem unfair. You've had so much in your lifetime. A very serious mental illness, alcoholism, losing your kids-- all very difficult things. And while it is unfair, your brother is probably doing what he feels is best. He probably has pain over it as well. He may feel that your coming back into the children's life could bring chaos because of the chaos he's seen previously. He's moved on in life, taken over the reigns of parenthood and for that, I would be eternally grateful to him. But it is hard because in doing so, he has cut ties with you. We don't know his side of it. But I do know, for kids I love, I would make very difficult decisions for what I thought was their well being. Or my own if he feels you bring so much along if he accepts you back into his life.
I'm very empathetic though to how this must make you feel. You are trying to build your life. This is a constant reminder of things past that have been troubling. I will say that an alcoholic can not 'still drink' and not have it be a problem. That is not what any addiction counselor would tell you. You are surviving and doing better for sure, but that you are still drinking is troubling. And with your mental health issues, this is something to consider. Can you purge alcohol from your life entirely?
I agree that sometimes things just can't be fixed. He just may not be willing at this point to risk going backwards in where they are now. I'm very sorry as I'm sure this hurts so badly. I'm really glad you are taking your medications and seeing a therapist. Keep doing that and keep the faith. Life will unfold and it CAN change down the road. But this is where it is now. peace and hugs
Melissa, this might not be fixable. You are indebted to him in a way you can never repay. You were mean to him as a child, and now he's raising your children because CPS has taken them from you. In my opinion, he holds all the cards and has all the power, but I'm sensing you are treating him as an equal in this relationship - which would be the case if he weren't raising your children. I think he should have the option to not have a relationship - have you expressed to him how incredibly grateful you are for his sacrifice, and that you could never repay him and you hope to earn his forgiveness? That might go a little further than "I want to get to know you". Blessings. This is hard.