Do I have a chance?

My ex has been MIA since June of 2003. He pays child support but not by choice and has paid nothing over the court order for back support owing me $10,000 in arrears. Not seeing the kids was his choice he just stopped showing up and I have all the documentation on this. I have sole legal and physical custody of the kids and he has reasonable visitaion (meaning what I think is reasonable I can give him). My DH has been dad for 2 years now since my kids were (18 months old and 2 1/2 years old) when we started dating. We have been married for 2 months and are looking at starting the procedure in February. My sons call my DH dad (by their choice). I have a feeling this won't be hard to get him to consent but if he doesn't do I have a chance? I have a feeling he would rather have the $700 a month in cash than his kids he doesn't see.:confused: I will have a lawyer and I am prepared to drop all back child support owed to me if he says no but I am ready to fight if need be.