Only the person claiming the child as a dependent is eligible for the Child and Dependent Care credit and expenses on their tax return.

I have a similar question — my ex is claiming my youngest this year as we alternate.  I am head of household and we both pay the child care and the children are with my over 65% of the time.  I know only one parent can claim - I thought it can only be the custodial parent?’  My ex’s accountant says he is entitled to write off daycare expenses on form 2441 bc he is claiming her this year.  Is this correct?

Yes, only the custodial parent can claim the child. The custodial parent is the one with whom the child spends the most time.

Read "Child of divorced or separated parents or parents living apart" in IRS Pub 503 on page 4.