Either you are the custodial parent or you are not. The custodial parent is entitled to be head of household and take the dependent care deduction (and the earned income credit if they qualify). The non-custodial parent is entitled to a deduction for the child tax credit and nothing else.
You can't claim the Child and Dependent Care credit if you are claiming that you aren't the custodial parent. Only the custodial parent gets to claim the expenses for care.
Here's the IRS guide for non-custodial parents.
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