How are switching on your TV? If it's by pressing a button which is actually on the set, I'm probably lost! (Except see my final paragraph below).
However, if you're using your remote control it seems obvious that the signal from your handset is having some effect on your son's TV. If it's only the 'on/off' button on your handset that is causing the problem, you could simply switch your TV on and off by pressing the button on the TV, thus avoiding the use of the troublesome handset buton.
When I gave my elderly friend a lift to her holiday accommodation in the summer, I showed her how to use the TV set and Sky box but I found that pressing the 'Channel guide' button on the remote control for the Sky box, switched the TV set to the wrong 'source' setting, so the problem of incompatible handsets is obviously far from uncommon.
If the problem is definitely not associated with the use of your handset (i.e. it's simply having your TV switched on which is causing the problem) then it's either r.f (radio frequency) interference from your set which is the cause of it (which is unlikely because modern sets have to be built to very precise requirements to minimise such interference) or, more likely, mains-born interference. If it's the latter, filtering the mains supply to your son's TV should fix the problem:
http://www.maplin.co....219077&C=SO&U=Strat15
Chris