Thank for getting back to me.
When you submit the 1040X to claim the dependents you are entitled to. (or alternatively to appeal the determination on your original tax filing), you include a cover letter.
On the 1040X itself, there is a space to put why you are filing the return. You will say you were denied dependents which you were entitled to claim.
However, in the cover letter you might say something like:
Please accept this 1040X which is submitted in order to claim dependents which were denied, but that I am entitled to claim.
My former spouse has apparently errored in claiming our children as dependents without entitlement. I am the custodial parent, am entitled to claim the children by virtue of:
1. Divorce Decree
2. The children lived with me for the entire year except for periods of visitation with the father.
3. I provided for and maintained the home for them during the entire year.
4. The children do not provide for more than half of their own support.
5. I have not signed any forms or statements giving my former husband the right to claim the children
Please find attached relevant pages form the divorce decree:
a. Cover page,
b. Signature page
c. pages of the divorce decree that speak about custody and taxes
d. school registration indicating primary residence of the children