Federal law always overrides state laws, or in this case, state family court orders. If you have custody more than half the nights of the year, you can claim your child. However, because your ex also claimed your child, you need to print your return and file by mail. The IRS will process the return and pay your refund, but eventually they will send letters to both parents starting an investigation and asking for proof of where the child lived. If you can prove the child lived with you, your ex will have to repay part of their refund with interest.
However, if, by claiming the child, you violate a court order, your ex can go to court and request that you be held in contempt, or forced to release the exemption, or be punished in other ways. The IRS will follow federal law, but the state court can issue other orders against you.
Also you need to be aware, I suspect you have not been giving your spouse form 8332. This is a dependent release, you must sign it and give it to your ex to allow your ex to claim the child. The parent where the child lives is the only parent allowed to claim the dependent care credit, EIC and use head of household status, those tax benefits can't be waived, released, shared or traded. If your ex was claiming the child without form 8332, they must have been claiming the child lived with them, and they may have received excess improper tax benefits.
