I can't seem to have the affect I'm looking for on a "Live Ubuntu"

I want to run it from the USB drive, a fully functional, fully upgradable version.

I do not want to use as a "trial version", or to set up a dual boot or run in a virtual system.

I have kids that are killing my computer & everything on my HD, they need their own OS & drive but don't have the $$$ for a laptop for them, I just want it to work on the USB the same way it works on the C: drive