You are not "entitled" to the Child tax credit (CTC). Under federal law, either parent MAY claim the CTC. If you can't agree on who will claim it, the law says the custodial parent gets to claim it. In your case, the judge has ordered you to "agree". In addition, the non custodial parent needs form 8332 to "prove" that there is an agreement. Usually, the judge's order is part of the overall financial settlement, and not an isolated thing. It can't be appealed to the IRS.
What you can do is disobey the judge and not give the other parent the form 8332. In that case, the IRS will give your the CTC, if you claim it on your tax return. The IRS will not help the non-custodial parent. His only remedy is to take you back to the local court for sanctions, which could include jail time for contempt
