As others have said, I'd probably carry a quality adjustable wrench (Crescent brand or similar) and a set of Allen-head wrenches. You can find these either bolted together (in a multi-tool) or sometimes connected to a key ring where they all dangle free and you can disconnect the one you need to use.

I can sympathize with the need. If you need to remove a wheel when out on the trail (to change a flat), you need to be able to turn that nut if it's not a quick release. The adjustable wrench should be able to do that. And kids seem to always want their seats or handlebars adjusted -- at least mine do. It's not EVERY trip, but it's not common for one of them to want their saddle slightly higher or lower, or the shifter twisted just slightly on the handlebar. Rather than make it a negative thing ("silly kid, set it before you leave the house!"), I keep it positive by showing them that bikes are easy to adjust and service and easy to customize to meet their need or desire, even if that changes mid-trip. The more they get accustomed to working on bikes, the more they're likely to ride.