To answer your question, IMO, I would think it unlikely that any of the BR babysat for one another.
As children, my siblings and I had a nanny and if our parents were entertaining, we made the occasional appearance. If they were going out, it made no difference to our regime! When we went to visit the grandparents, it was a duty and we were not expected to enjoy it
, nanny went with us.
Even with my own children, I think the parents would have fainted if we had asked them to babysit!
I also wonder if they would have known how to look after them to the same standard!
We have been trusted with our grandchildren for short periods of time but, nanny is never that far away and 'hovers', especially if we are around the horses or BoP!