You will have to follow the court order, or be liable to contempt of court. I do not know which NYS supreme court case you are talking about. If you let me know which one, I can read it and give you an opinion about it.
However, in general, the IRS position on this matter is, that the IRS acknowledges the courts right to determine how the children can be claimed on taxes, it has to be within the meaning of current tax law.
So for example, the IRS stated position on the divorce decree, is that a non-custodial parent may claim the children using the divorce decree as a basis, if that decree contains the content and language or words to the effect of the form 8332. In that case the IRS recognizes the right of a father to claim the children provided they are otherwise entitled.
Under special rules for divorced and separated parents, the IRS allows the non-custodial parent to file for the children as long as one of the following 3 things are in place:
1. a form 8332 is signed by the custodial parent.
2. a statement containing the language of form 8332 is signed by the custodial parent.
3. a divorce decree orders it and the divorce decree contains the language, and content of the form 8332.
Your divorce decree cuts to the chase, and says you need to use a form 8332, and allow your ex to claim the children for dependency. This is not determining a tax issue. It is not awarding an exemption where one does not already exist in tax law or the IRS instructions. The court is recognizing that tax benefits are a custodial issue for divorce courts to consider.
If he court had said this about someone not entitled to take the exemption, then the IRS could exclude itself from following the order. But in this instance, he is otherwise entitled, and so you have to follow the court order, unless you can get it modified.
I can not tell you if you would be successful at modifying it. Your basis is that the court lacked jurisdiction. In my mind, if you are ready to pay the expense, of landmark court decisions, without a guarantee of winning, then you should go for it. This has the potential of getting big, because not only would you be challenging the court on jurisdiction, but also no the divisibility of tax benefits, that someone is otherwise entitled to already, by the court.
Think of the far reaching effects. Think of 10's of thousands of divorce proceedings every year, where divorce courts are deciding who pays the capital gains on property settlements during divorce, or how court orders are written so that one party or the other, or both, can avoid taxes or incur taxes on division of 401(k)'s, and so forth.
The issue of who gets the exemptions for separated and divorced on the IRS side, is not dependent on whether or not the non-custodial parent fulfills his or her visitation option, or whether or not the non-custodial parent is current on child support. It is based on the fact that the non-custodial parent as sanguinity, and is allowed to if one of the three conditions previously stated are met.
The IRS is on record as having said if the divorce decree is within compliance with form 8332 and the tax law, the IRS will recognize it and enforce it. However the IRS also is on record as saying they will not resolve issues related to problems with the decree itself.
So if you want to modify the order, to take away his right to claim the children in alternate years, then that requires you to ask for the modification. I know I said earlier that your basis would be on lack of jurisdiction, but I said that with respect to your comment about the NYS supreme court. You can also ask for modification, simply that he is not fulfilling his visitation and support requirements and you would like wider discretion in determining for yourself when he can claim the children in any give year.