This is a case where federal law dictates the answer. Under the Internal Revenue Code, the parent who is the primary custodian gets to claim the children. Sometimes in divorce cases we make provisions regarding who gets to claim them, but the federal government doesn't care one bit about what a State court rules.
So, to answer your question, it sounds like you get to claim them under federal law. You may, because you are a nice person, allow her to claim them, but that is solely your decision. If you both claim both children, then ultimately, when the IRS flags your returns, you sir would win the battle. At least that is my understanding of how that works.
Good luck.
Answered on Jan 11th, 2013 at 11:35 AM