You don't need to have a dependent claimed on your return in order to qualify for the Earned Income Tax Credit and Child and Dependent Care Credit.
The credits may be claimed by the parent who has custody of more than half of the year. Typically, eligibility is determined by your custody agreement.
The other noncustodial parent may claim the dependency exemption for the child, if you, the custodial parent, releases a claim to exemption. Also, the noncustodial parent may claim the child tax credit for the child if the requirements for the credit are met.