The divorce decree says that I can claim one child for tax exemption purposes and he gets to claim the other one. It 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 absolutely everything by myself 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 pay for our basic expenses and can't afford one. I was hoping there would be a way in cases like this where the non-custodial parent is gone.

If you are paying 100% of the support for your children, claim both as dependent on your tax return. If their father has a problem with that he will have to establish, with the IRS, that he paid for at least part of their support.

While, I'm inclined to agree with AK, I'm concerned that the divorce decree specifically deals with this issue. I would cover my bases by petitioning the court to amend the decree. You should be able to do this yourself and the cost will only be a filing fee.