The only parent who can claim the dependent care credit is the parent who had actual physical custody more than half the nights of the year, regardless of what the divorce decree states. See publication 501 under "special rules for children of divorced or separated parents." https://www.irs.gov/uac/about-publication-501
It's hard to simplify here, but basically, there are 5 tax benefits of a dependent; the exemption, the child tax credit, the dependent care credit, qualify for EIC, and qualify for head of household. The parent who has custody more than half the nights of the year automatically gets all of those benefits. The non-custodial parent can only claim the child tax credit and the exemption, and only if the custodial parent gives them a form 8332 release, or if they have a qualifying divorce order from 2008 or earlier that contains certain specific language.
If you don't have custody more than half the nights of the year, you can't use the dependent care credit or use a dependent care FSA.
In turbotax, you would answer the custody question "how much of the year did you have custody" with "6 months or less", "are you claiming the dependent from a form 8332"--yes. Turbotax will not allow you to claim the dependent care credit in that case.
If you are the custodial parent of both children, and both children were in care, then you provided care for 2. You would answer the custody interview by saying you had custody for 7 or more months (more than half the year), and you are giving the other parent a release. That will remove the exemption and child tax credit from your return but allow you to claim the dependent care credit, head of household, and EIC (if you otherwise qualify.)
If the children lived exactly half the year with each parent (183 nights in 2016; impossible in a non-leap year) then only the parent with the higher income is automatically entitled to all the dependent benefits and the other parent can't claim anything without a waiver, and the same rules for the dependent care credit apply.
If you are not the custodial parent, but you and your ex are putting down on the tax form that you have one dependent each, then you would claim care expense for only that child. And one of you is committing tax fraud and the other one of you is aiding and abetting tax fraud. You probably won't get caught, unless one of you blows the whistle, but if you get caught, you can owe back taxes, penalties, and if EIC is involved, you can be automatically barred from EIC for 2 years or more.
