I am so sorry.
I believe your boyfriend may have been right to break up with you. He's obviously not ready for a relationship. He is not sensitive to the needs of others at all, not even his own children (who will be very affected by this breakup), and he's being incredibly self centered. His behavior is very immature. Breaking up on the phone? Running away when things get difficult? Breaking up so HE doesn't feel guilty? It's like he's trying to push his own guilt off on you. Is this a grown man? Or a teenager?
Notice that when his kids are getting out of control and into trouble, they are brought to their mother, not their father. Could it be that he isn't a great father figure? That he can't help them work through their issues because he is too caught up in himself?
Every word of your letter makes me think there is not only more going on here that you aren't aware of, but that this guy is really poor boyfriend material, and awful husband material.
Walk away. DO NOT continue to contact him. Let him go grow up on his own - you can't do it for him. If you display any need at all, it will probably push him away, because he really needs to have it all about him.
Perhaps he will realize what he's lost and return. By that time, I hope you've had some time to adjust to his absense, and time to consider if this man is really all that good for you and your family. Once the painful fog clears, you may find that this was the best thing that could have happened.
Focus on you now. Make yourself happy, without the benefit of a man. You don't need him or his painful baggage in your life. Go out and do something that makes you happy. Treat yourself. Focus on your kids, too. Any time you feel that pain raise up, give yourself a few minutes to grieve, and then STOP. Go on with your life. It will get easier. And you will probably find that while this guy may have a lot of redeeming qualities, he is not ready for commitment, he is not ready to give himself to somebody else, and he is not ready to be a parent (regardless of what nature has given him). He isn't what you need. He is never going to be there for you. He isn't there for your kids. You deserve so much better. There is someone better out there. Someone who isn't so needy, so selfish, so absent.