Hello C.,
I have a lot of empathy for your desire to change the situation between yourself and your daughter. Congratulations on recognizing that you want something different for your relationship and something better for her.
I can only speak from my personal experiences, and will be as brief as I can. My childhood was very, very troubled due to the choices both my mother and father made. They split up while she was pregnant with me, and have remained so. As a young adult (and up into my early 30's) I had a lot of personal issues that were fallout from my early years. I sought counselling in my late twenties and tried to address some past events with my parents. My father was willing to go into a counselling situation with me. It was, at times, excruciating work, and I am happy to say that while our relationship isn't perfect, I now have reasonable expectations of him, of who he is, and understand him better. It's been a blessing to get to know who he is past my anger and hurt, and for him to get to know me better.
While I invited my mother into counselling with me, sadly, she refused. When I approached her about incidents that were very traumatic, she was very defensive and made excuses, blamed others and refused any responsibility. It seems that no one was traumatized by her choices more than she was, and no one has the right to ask for her help in their own healing. Nonetheless, I've made it clear that for us to have a relationship, counseling is necessary. I didn't want to blame her, but to heal our relationship. I haven't heard from her in nearly ten years.
I'm glad you have made the choice to help your daughter, and I just want to say this, as a daughter to a mother: stick with it. It is hard, it feels really dark and ugly sometimes to go back to mistakes that we have made, but it is so, so worthwhile for your relationship. Having that third party in the room who will validate everyone's feelings is so essential, and doing the hard emotional work is so important. I am not one to share my personal life to strangers, but I think you really want to know what to do. Be real, be honest, be invested in the process, even when it makes you angry or scared or feel awful. I did it with my dad and am grateful for it every day. I know he is too.
I know you are trusting in Christ, so let me add one more thought: if you take those steps out there, God will build a bridge for you. You may not see it for a long time, but it will be there. Give your daughter a lot of time to take those steps toward you, and give this process a lot of time. Hopefully, she will move closer to being the person she wants to be, as you become the person you want to be.
My very best to you,
H.