least - you are to be applauded for acknowledging what happened. I think dothi's advice of having patience and acting consistently is your best way forward. Show that you care and love your children through quiet, honest, consistent, reliable actions. Personally, I wouldn't share your personal pain with your children, I would keep that to yourself, they are still looking for you to be their Mum and to put them and their pain first - just MHO.
My AF and codependent mother have never acknowledged their responsibility for the damage my childhood did to me. Denial and self-pity still exist in spades. I have had to go to the other extreme and let go of the fact that I will never get an apology and never get the parents that I wanted and deserved.
Your way is better because I have moved forward to the point where I don't like my mother as a person and I'm not interested in having her as a part of my life.
You are a brave, courageous person to look at the effects of your actions and I admire you for that. Well done, IWTHxxx