Nanny Poppins could leverage this with an API for the approved/vetted sitters that are available for that set of parents.
That's actually a pretty neat idea!
A big part of why I consider HN worthwhile to read and post to: we only have time to even attempt executing on so many ideas, but maybe someone else is working on it. Like a big "take an idea, leave an idea" jar.
Since couples tend to collect a small number of sitters and stick with those - frequently friend-of-friend's older children within social groups (church, suburban neighborhood, etc.) - the most tractable approach is more likely to be a calendaring and booking system for sitters vs. a "vetted employee" paradigm.