After you file

My situation is slightly different, but I'm having the same fallout.

I am a stepparent to 2 children who spent 9 months of 2019 living with their father and myself (we are married). They had limited visitation with their mother in that time (no overnights). She regained 50/50 custody in Oct 2019 and then took full custody in November 2019. She has claimed them both on her taxes, my claim for them was rejected on e-file.

I file married filing separate due to my husband being a disabled veteran who gets VA benefits and they are not taxable.

By IRS rules it seems the children should be mine to claim for 2019. Am I correct and how do I appeal?

Thanks for any help.