Hi Powerful Horse,
I am not from Laminar Research; just a flight simmer.
In reading your problem I am of the opinion that you have 2 password requirements to activate X-Plane.
The first password required is when you turn your PC on. My reading tells me your son has his own password. The use of a password when the PC is activated has no impact on the running or starting X-Plane. I have this system in place.
The second password requirement is when x-plane is started. This password is called the "Kiosk" mode and details can be found in the manual at https://x-plane.com/manuals/desktop/#kioskmode The purpose is to restrict others from making changes to your setup. Have you activated this system?
I don't use or activated this facility as I don't have others using my flight simulator PC. If someone else activated x-plane PC they could without any password requirement.
If you have activated this option you may have to unlock the facility so your son can use X-plane or give him your password so he can use x-plane. My reading of the manual and other questions raised in this forum suggests only one password can be issued. This interpretation may be wrong.
Good luck in solving your problem if my assumptions and suggested solution(s) is/are wrong.