Rejected taxes due to depended children on both mother and father returns

Due to the fact the other parent already filed with all 4 of our children without consulting me. I files 2 of the 4 children, got rejected by Federal and State because they were already claimed on their mothers taxes. We were never married, but I have always claimed the children, either all 4 of them or just 2 of them depending on if the mother had income that year, which didn't happen very often. We haven't been together for the last 6 months of 2019.  But I was the sole provider the first 6 months of 2019. Did she have the right to  claim all our children without consulting me, knowing I would of claimed 2 of the 4?? She was just trying to beat me to the tax man, which is both of our tax person. What's wrong with that picture.....