In that scenario you'd have to apply the STOP acronym and, like, think for a bit and collect what information you had. A lot would depend on the detailed threat, the age and ability of the kid, etc. Initially you said they were at school, but later you say they were visiting friends. It surely makes a huge difference. If they are scattered around, they are reasonably independant and able to look after themselves, and their being missing is not an indicator of special problems. If they are at school, then surely they shouldn't go missing so that sounds like a more worrying scenario to me.

I don't actually have children, and don't want any, so I'm inclined to be cavalier about it. In a disaster I would tend to trust the kindness of strangers - but then I don't live in America. At age 8 or above I'd hope they were able to look after themselves to a large extent and be prepared with the basics (eg the difference between asking an unknown adult for help and accepting help offered by an unknown adult). In general I'd expect the child to become very distressed and unhappy if abandoned, but most experiences would be just as survivable whether or not I was there.

Here's one special data point I came across recently: If you are evacuating an airplane when you are separated from your kids, you shouldn't go looking for them until you are away from the 'plane. That's because one person moving against the flow can block the egress of many.