Sorry, but I can't find any reason why anyone would need to bring their child to a call. I understand rural EMS, really. I grew up in a town of 128 people depending on traffic. Our zip code was only 3 numbers long. Depending on how good of a golfer you are, you could drive through town in two different ways.
Ok, enough.
Anyway, if there weren't enough volunteers to respond, mutual aid was called. Granted this was fire & first responders. We didn't transport, ever. So it's not like there was a risk of no response. Even if we were responsible for transport (shudder) there would have been shifts of coverage to ensure the people responsible to respond were prepared.
In a case of fire, mutual aid was called anyway unless it was a car fire or something minor.
As far as ride-alongs for minors. This seems like a bad idea. Very bad. There's no reason for it. If they want to learn about first aid, they can join the scouts. If your service is actually using children for ems or fire, close your doors and walk away. If I were at your fire for mutual aid and I find out you have a kid responsible for fire suppression, we're going to have a serious discussion about our mutual aid agreement as soon as the fires out.