Claiming kids for taxes-messy situation
ITA with this. It very specifically says in DH's divorce agreement, "if the parties cannot agree, they go by the divorce agreement." Your DH and his ex cannot agree; it should be your DH's turn. It's no use arguing with some people about what is "fair." The judge thought alternating years was fair. That makes sense to me!
This is the wrong part of the year to be making these kind of changes. Even though any fees you might encounter are likely minimal, the Court has ordered this. If she thinks its not fair, she can petition the Court or wait until the next cycle when your DH can evaluate her request and make preparations (ie change withholdings), if he chooses to agree to the change.
This is not about what's fair. That he has another child to claim is not the point. The Court has ordered this, the end.
On an "if we're going to deviate from the Court's order" note, I personally find alternating to be a pain in the rear. To me it should be claimed by whichever parent is in the higher tax bracket (considering real circumstances, not the hypothetical ones used for calculating CS, if there's a difference) since this provides the most benefit for the child! My DH agreed to alternate to "make peace" but it "costs" her over $1000 each year in CS+taxes because he gets more tax savings than she from claiming a child and he would owe more CS (well more than she gets in tax savings) as a result ... it would be a wash for our budget but it's real money not available to DSD to make this peace.