I am not from Laminar Research; just a flight simmer who does not use a Mac
You have not indicated whether you have a digital download version or a disc version.
If you have a disc version you have to have disc 1 inserted at all times in your dvd drive for it to operate otherwise it will operate in demo mode which has a 10 minute time limit. When running digital download version you have to be connected to the internet at all times as the software performs a silent check on the validity of your copy of software. Again if you don't it will automatically revert to the demo mode.
X-Plane does not require individual user passwords unless Laminar has changed the system in the last couple of upgrades (highly unlikely). I don't have the latest version to confirm a change has been made. If it did require individual pass words as you are suggesting then Scout groups or Air Casdet groups etc would also be in trouble in trying to login for each individual user.
Your comments in asking for the product key for each application suggests to me you are not connected to the internet at all times when running X-Plane. If it is still an issue I would also suggest you run X-Plane under your name and then allow your children to use the software.
Again if it remains an issue you may need to revisit your parental controls on your Mac.