First of all, the Child Tax Credit and the Child and Dependent Care Credit are two different credits. You are asking about the Child and Dependent Care Credit. The Child Tax Credit has nothing to do with daycare expenses.
Because there can be two children, and possibly multiple care providers, you have to enter the total amount you spent for each child, and also enter the total amount that you paid to each care provider. The combined total for both children has to equal the combined total for all providers. It's not two separate credits, and you are not claiming the same expenses twice. It's just two different ways of splitting up the total amount that you paid.
