Just brainstorming here, maybe if they jump through the hoops to take a selfie it could grant them an extra 5 minutes or something to that effect. Partly why I say this is it may take a few more steps and those steps might be bypassed and or canceled by the user on purpose or on accident. Thus a little incentive to follow through and not rush or cheat.
Thinking of a selfie, you could probably text your iCloud/phone number with the last photo/selfie on completion. Or just save it on device.
If this does get more complicated and interesting. It might be worth putting all this functionality into a shortcut and then select the ‘run’ action and just run this shortcut for each ‘open app’ automation you create for the kids.