Yes, you can still claim the child care if the child lived with you for more than half of the year (it means you are custodial parent). As a custodial parent, you are allowing the other parent to claim the child for the year. You gave up the dependency and child tax credit but still qualify for the dependent care, EIC and Head of Household status.
In TurboTax, add the child's personal information and follow the interview process. Let the program know that dad is claiming the child for the exemption, the program will take care of the rest.