Here's a bit of infomation that you may find helpful, if not useful.
First, understand that the IRS has rules that pertain to who can claim the dependents of a divorced or separated couple. Those rules are based on federal law. Only a federal judge can "over-ride" those rules. Since federal judges do not handle divorce, separation or custody cases I can tell you with 100% certainty that such an "over ride" will never happen. But that doesn't leave a state judge or lower level judge completely powerless.
The IRS rules on this are covered in detail in IRS Publication 504 at https://www.irs.gov/pub/irs-pdf/p504.pdf
Basically, you have the custodial parent and the non-custodial parent.
CUSTODIAL PARENT: The custodial parent is the one with whom the child stayed with for more than 182 nights of the tax year. The nights (not days) do not have to be consecutive. Temporary absences such as hospital stays, being away for school or spending a night at a friends house count for the custodial parent also. If the parents separated during the tax year and neither parent meets the 182 nights rule, then it's the parent with whom the child stayed the most nights of the tax year.
NON-COSTODIAL PARENT: The non-custodial parent is the parent who does not qualify as the custodial parent.
Now the non-custodial parent can claim the child *PROVIDED* the custodial parent provides the non-custodial parent a signed IRS Form 8332-Release/Revocation of Release of Claim to Exemption for Child by Custodial Parent. Without that form signed by the custodial parent, the non-custodial parent can not claim the child *no* *matter* *what*. This is where a lower level judge can be influential.
The judge can lawfully order the custodial parent to sign the IRS Form 8332. If they refuse, then the judge can find them in contempt of court and do whatever the laws they are bound to will allow. For example, the judge may be able to incarcerate the custodial parent until the sign the 8332. Or they may be able to fine the monetarily for every day they refuse to sign. There's probably a number of other things they can do also. It just depends on the laws of whatever state you are in.
But the bottom line is, if the non-custodial parent does not have a signed 8332 from the custodial parent, then the non-custodial parent flat out can not claim the child. Period. End of story.
One note of importance here. While the non-custodial parent may have a signed 8332 from the custodial parent allowing them to claim the child as their dependent for the $500 child tax credit, the *CUSTODIAL* parent still has the right to claim the EIC (Earned Income Credit) for that child. The non-custodial parent CAN NOT claim the EIC for that child.
