DoninGA is correct, you have to file a paper return and let the IRS sort it out. The IRS will pay your refund in the normal time (for a paper return). The "sorting out" will come later. An ex's girlfriend cannot claim a child, unless the child lived with her ALL year. Even then, she would not be allowed the child tax credit or Earned Income Credit or child base stimulus, because they are not related. She would only get the (non refundable) $500 other dependent credit.
For tax purposes, there is no such thing as joint custody, regardless of what your legal agreement says. The IRS requirement, to be custodial parent, is that the child live with you MORE than 50% of the time. One of you has to be the custodial parent and the other the non-custodial parent. The IRS goes by physical custody, not legal custody. Yes, the IRS expects you to count the numbers of nights the child sleeps at each parent's home.
The IRS does not enforce court orders ("the family court judge denied them the right to claim him"). It goes by physical custody, so if the ex had the child the most and it was him who claimed the child (and not the GF), the IRS will side with him. Your only remedy for violation of a court order is to go back to the judge.
The custodial parent has first priority on claiming the children on her taxes; regardless of the amount of support provided by the non-custodial parent. The IRS goes by physical custody, not legal custody. The non-custodial parent can only claim the child as a dependent if the custodial parent gives permission (on form 8332) or if it's spelled out in a pre 2009 divorce decree. Even if a divorce decree, dated after 2008, gives the non-custodial parent the right to claim the child, he must still get form 8332 from the custodial parent. A properly worded decree should require her to provide that form. https://www.irs.gov/pub/irs-pdf/f8332.pdf
There is a way to split the tax benefits. For future negotiations with the other parent (and maybe even for this year) the following info may be of use:
There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.
Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the dependency to him.
