I am not as seasoned as many of the people here but here are my thoughts.
What do *you* want? Do you just want him back or do you want to be a happy, fulfilled person, with or without him?
If you just want him back, then go ahead and jump back on the Kevin Merry-go-round.
Otherwise, you need to take a good hard look at yourself and set boundaries, decide what *you* want in a man and make sure he lives up to that. Tell him that you are focused on taking care of your children and yourself right now and if he wants to be part of your life he'll have to man-up, like providing financial support for his little girls, helping you with Doctors appointments and demonstrating that he is a stable source of emotional support for you, rather than a the trainwreck he has been.
I'd have friendly civil conversations with him on the phone, let him see his kids, let him participate in activities with the kids and let him show you (over time) that he can be a husband and a father rather than a impulsive little brat.
Most importantly, you need to get to a place where you won't be left destitude and empty if he pulls this crap again.
Do you even want him back? You asked what to do but you haven't even said if you want him back.
Grasshopper, I don't know if you have read Why Men Love Bitches, it isn't about being a bitch literally but rather about how women need to not depend on men for everything in their lives. The better developed one is as a woman the more one has to offer a man in the way of companionship.
