Deductions & credits

Ok… tell the people who need to look at your bloody tax return that the other parent is claiming the children as dependents per the IRS rules and regulations. The fact that they don’t show up on your tax return is immaterial since they do live with you. As mentioned in the other answer, show them pictures of the kids beds with them in it, paid bills for them with the Apartment address on them, affidavits from the neighbors that see them come and go, etc. etc. etc. get creative.