After you file

here's where the Courts and the IRS differ.  the IRS says the custodial parent gets to claim their qualifying children despite any court order to the contrary. the IRS says for the non-custodial parent to claim qualifying children the custodial parent must supply signed form 8332 to the other parent which that parent must include with their return.  amending your return won't do any good if she's the custodian and hasn't furnished you with the form.  it will be rejected since the kids have already been claimed by her.  on the other hand if you are the custodian do file an amended return - eventually you'll get a refund and she will have to pay taxes, penalties and interest. what can you do if she's the custodian - see a lawyer - the IRS sees nothing improper in what she did.  since she claimed them in 2019 she's likely to claim them in the future.  only the courts can do anything.