My ex and I each claim one of our two children on our taxes, but we split all costs and custody equally. How can I write off what I spend on child care for each child?

In order to claim the Child and Dependent Care Credit, you must be the custodial parent. You also must have been the parent who paid the expense. If you have two children and you share custody, you could agree that one child lived with one parent for more than half the year, and the other child lived with the other parent for more than half the year. Each of you could only claim one child’s daycare expenses. You can’t divide the expenses for both children and each claim half.

Please see this  IRS link, under Child of divorced or separated parents or parents living apart.