Back somewhat on topic, not to be prickly, but if the child was sick and needed a babysitter for the day, is picking a new partner to help you any worse than asking the 12 year old neighbor to do it?
It's always worrisome to have someone new other than family look after the kids whether or not the kids are in your custody.
I'm not sure I'd accept an agreement that included such clauses, though basically my ex has demanded pretty much that information already anyways.