I'm not a tax expert but I'm in the same situation. My understanding is that in the section where you claim dependents, you only check the box for "amount for eligible dependent" for one child (presumably you have agreed to which one in your agreement). The other parents checks the box for the other child. You can still claim childcare and activity expenses for the kid you're not claiming as a dependent.
There are other ways families manage this, such as alternating years, but this is how I understood you want to do it. Hope this helps other separated and divorced parents!
