My spouse and I are recently separated. We want to divide child care expenses on our taxes. Can I just claim half and he claim half? How do I report?

To claim childcare expenses, you need to report the child on your return as a dependant. And, only one person can claim a child as a dependant at a time. So, only one of you can claim childcare expenses, and the spouse that claims the expenses can only claim the amount that they paid.