I really feel for you Quinwa, as I have gone through something similar with my daughter. Her father and I separated when she was 13, and she went through a very difficult few years after that, which included suffering abuse at the hands of her father when I left. At the time I thought I was doing the right thing by her as we'd recently moved to the area, (a long way from 'home') and she'd only just settled in at her new school, made new friends, etc. Never in a MILLION years would I have left her with him had I suspected what would happen. I believed at the time that she would be just as happy with her dad as she was with me, and wouldn't have the trauma of changing school, friends. etc again. Having gone totally off the rails due to her experience, which she obviously blamed me for, she got together with a lad who she later married and had children with. Since the events with her Dad, we have never had an easy relationship, and she always seemed angry with me, which I could totally understand. However, over recent months, she has found herself in an unhappy marriage, and finally plucked up the courage to leave, taking her children with her, but only because there was another man in the background. This was history totally repeating itself, and having continued to stick with her through thick and thin, insults, fallings out, etc., over the years, she has finally realised that I struggled in EXACTLY the same way that she has done, and now that she has left her husband and is in a happy relationship, she is a changed woman, and has finally come back to me as the daughter that I knew and loved as a child.
My advice? Stick with it, don't keep apologising, but be there for her through thick and thin, and hopefully she will eventually realise that you are human, and made mistakes, just as she will inevitably make mistakes in raising her own children.