If you were able to take a child care credit for this child, that means you said the child lived with you more nights out of the year and you were the custodial parent. Only the custodial parent can claim the child care credit, the Earned Income Credit and Head pf Household for this child. The noncustodial parent can at most, receive a $500 nonrefundable credit, meaning she can't get it back in cash, and the child tax credit.
You cannot claim a child care credit for paying a parent to watch their own child. Yoy would need to amend your return to remove this credit.
https://ttlc.intuit.com/replies/3288565
If you're an unmarried couple living with your child, you can't split child related items in any way. Only one of you can claim everything related to the child.
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