That sounds tricky, especially since you have other folks and a dog who aren't quite as tolerant of the insects to think of. Depending on the ages of the children, perhaps some simple education about the insects being harmless as long as you don't mess with them would help? The dog is trickier. Perhaps there are certain times of day that the cicada killers are less active that would be better for the dog going out until you figure out a better solution? Maybe the dog tried to eat one and got stung? I wonder if something like Rescue Remedy for pets could help calm them down so they can learn that as long as they don't mess with them, they aren't a threat?
While I totally see why you'd want to check their numbers given the circumstances, I do wonder if that's a good idea. If there are that many of them, it seems to me it would indicate a ridiculously high number of cicadas and their larvae. I guess I'm saying, if you remove the cicada killers, you might just have a cicada overpopulation issue in some years. Just something to consider.
There is some good information about the life cycle and habitat preferences of the cicada killers here:
https://entomology.ca.uky.edu/ef004
They suggest that drenching the area around their burrows with just
water could sometimes cause them to abandon the site, because they don't like wet soil. Maybe worth a try in areas where interaction with people and pets is most problematic? Then if it works, you could try just keeping up with more regular deep watering to discourage them? It sounds like even if you killed all of them, as long as the site is attractive, more will show up. So changing the conditions to not favor them seems the best long term solution. Wet soil and reduced sunlight seem to be what they don't want and are easiest to address.