It depends. At the end of each dependent entry, the program would have shown whether the child was a dependent or was a Nondependent-for EIC and Child care only. If for EIC and Child care, then the other parent can still claim the child as a dependent but not for Earned Income credit or the Child care Credit. Those would show on your return.
If you and the other parent are an unmarried couple living with your joint children, then only one of you should have entered everything about the child and the other parent should have entered nothing.