Ex Husband incorrectly claimed both dependents and it's affecting my return.

My ex husband mistakenly claimed both of our children on his return. I tried to go ahead and file with one of them, but my return was rejected. He states he submitted an amendment, but hasn't heard anything about it. If I fix my return and remove my daughter, I'll owe the IRS. If I am able to claim her and head of household, I'll get a refund. 

 

Do I need to go ahead and file with owing the IRS and then submit an amendment of my own? 

 

thanks!