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Let's start with an example child support order of $1000 per month plus the non-custodial parent gets to claim the dependent every other year.  That saves the non-custodial parent about $2000 every other year.  Personally, I would rather reduce the child support to $900 per month and let the custodial parent always claim the dependent, as it turns out the same in the end.

But, in this situation suppose the custodial parent does not allow the non-custodial parent to claim the exemption -- that means the custodial parent gets $2000 more on their tax refund that ultimately comes out of the pocket of the non-custodial parent who can't claim the dependent.  The custodial parent has basically "stolen" an extra $2000 in child support from the non-custodial parent.

Family court judges tend not to like this kind of behavior.

The parent here was ordered in 2017 to waive the dependent for 2017.  What is not clear to me is how this was done -- if the custodial parent had given the non-custodial parent a signed form 8332 AT THE HEARING in March 2017, it can't legally be revoked until the start of the next tax year.  So apparently, she did not give him the form at the time and the court didn't order it, so when tax season rolled around, she refused to give the father the form, and claimed the child.

Again, family court judges tend not to like it when parents ignore their orders.

The IRS employee was correct that from the IRS point of view, the custodial parent never has to sign the waiver if they don't want to.  But the employee, and the mother, both failed to take into account that, while the judge can't authorize the father to claim the dependent without the form, the judge can order the mother to sign the form or be held in contempt of court.  It sounds like the mother needs a new family law attorney who will tell her that not following the judge's order is a bad idea.

So now it sounds like the judge is extra-annoyed, and is penalizing the mother with an extra 5 years releasing the dependent exemption to the father.  This is perfectly within the judge's right.  He or she can issue broad orders and penalties to force the parties to comply with court orders.  (I'm sure that if the shoe were on the other foot, and the father was missing payments or refused to return the child after visitation, the mother would appreciate a judge who expects their rulings to be followed.)

To say it again: the judge can't authorize the father to claim the child without a release, since that violates federal law.  But the judge can order the mother to sign the release.  The judge could also reduce child support, change visitation, fine the mother, or put her in jail, for violating the court's orders.  

There is nothing that a tax lawyer can do for the mother.  The dependent rules are crystal clear.  If she signs the form, the father claims the exemption, and if she doesn't sign the form, she can claim the exemption.  The IRS will be happy to apply the federal tax law either way.  But if she doesn't sign the form, she can be punished by the judge, so if she wants to modify the order or change the support arrangements, she may need a new family law attorney.