I do understand how exhausting it is trying to co-parent with someone who is suspicious of everything you do, and hates the very sight of you.... I am also very aware of how it effects,or is it affects the children. If you can focus on the best interest of the children, just maybe you can forgive (in time and in YOUR time) his actions during the time he was at his worst. I know you can't forget what he has done, but the choice is yours whether you will continue to forgive.
I know I would just melt if I were to ever hear just one appology, and now it seems you have two, or at least an email confirming the reality of his original appology. This is promising....
As he confirmed his appology, why not try to confirm your acceptance, to reassure him that you are willing to meet him half way, and work for the sake of the children..... it's a pretty good reason, as you already know. There are so many situations in the future to work towards, that even if you continue on separate paths, the girls will be so much more at ease if you two can be civil towards each other, like school graduations, marriages and Grandchildren..... the work you do now, will be so worth the effort.
Understand, that he will have relapses, he will be spooked easily, and be very insecure about your acceptance of him and those things he has done.... patience and tolerance are necessary, as I know you have these things in reserve, within your own strengths.
One small step at a time, be as reassuring as you can be, but again, remain true to yourself. There's no reason to bring up the pain you have had at this time.... he's not strong enough for that now, although I am perfectly aware the hurt you have and have felt, needs to be heard, and should be heard, now is not the time, unless it is here or with a counselor.
You are doing great! Patience and baby steps my dear.....
Blessings
Jeremiah 29:11 For I know the plans I have for you.........
