Q. In this case would it be easier for me to completely leave the child off my return that receives the credit?
A. Yes, if it's been decided that the other parent will be the one claiming the child for 2022. Leaving her on, just invites mistakes being made. You are correct, there is no benefit to entering her.
As to your ex claiming the child care credit. The general rule is that a taxpayer must actually make the payment (as well as be legally liable to pay it) to get the deduction. However, there is a tax court ruling that seems to say that she can take the deduction even if she was the one that actually paid it under the theory that your paying the expense is just another form of child support and it was her money that paid for it.
