You thank your lucky stars that he is gone, gone, gone. Don't try to hold on to what you don't have. Your children do not have another parent in their life - you are it. Accept that and know that it's enough.
Really, he sounds like a total loser. Would you really want him around? Picture what life would be like if he were nearby. You know that it wouldn't be the healthy, positive, shared custodial relationship that you yearn for. He would still be failing your kids, just in-person and more frequently. Not picking them for his weekends. Not paying for child support. Promising to show up for a ball game or a play or a dance recital and missing it anyway.
Why do you have contact with him at all anyway? If he's not paying child support and not visiting your kids, what role does he have in your life (or theirs) other than antagonizing you and failing you and breaking your kids' hearts? Cut off all communication and let your children know that parenting is a responsibility that both mothers and fathers share. Part of that responsibility includes, yes, paying child support when you don't live with your children. When someone doesn't pay support or honor a visitation schedule, that parent is choosing to not be involved and it's his loss.
Sorry to sound harsh but you really need to let go so that your kids can let go too. They don't have a father - big deal, a lot of kids don't and life goes on. Focus on what you and your kids DO have and ignore the guy who opted out (other than keeping a child support claim open, which you should, of course, do). My oldest son's father left before he was born and honestly, it's the best thing he could have done for us. He would have been an irresponsible nightmare if he were here so I'm glad he's gone and we avoid drama. I still have a child support case open but other than the occasional letter from the child support agency (informing me that they still can't find him LOL) I don't give him a second thought. Don't give him any more power over you and your kids - he's made his choice clear. You don't need him anyway.