Can I claim both children when filing my taxes if other parent is out of the picture?

The divorce decree says that I can claim one child for tax exemption purposes and he gets to claim the other one (I went along with this since I thought he was going to pay child support). The decree also says that he pays child support and gets visitation days but he seems completely gone. He hasn't paid child support this year (quit his job) and hasn't requested to see his kids. I pay for everything and would like to be able to claim both children when filing taxes next year. Is there a way to do it without incurring in lawyer costs? With my income I just cover our basic expenses and can't afford a lawyer. I was hoping there would be a way to regain the right to claim an exemption in cases like this where the non-custodial parent is gone without needing a lawyer.