Load Toad,
For BA at least, Capot has got it pretty much spot on. That's exactly the way it still works although apparently, we're no longer allowed to threaten execution. Something to do with PC stuff and them having rights now.
If there should be a diversion to an airport with none of our staff, the children will stay with the crew, even down to us sorting a hotel room and staying with them if an overnight stop becomes necessary. In those circumstances, you would obviously be contacted not only for your peice of mind but also in case of special instructions. In the case of a local diversion where the passengers are then bussed the rest of the way, a crew member will be taken off the aircraft and nominated to accompany the UM on the bus. In other words, your child/children will be accompanied every step of the way.
I don't know how it works on other airlines but I'd imagine it's pretty much the same throughout the industry. I hope that puts your mind at rest somewhat.