I was a volunteer host once in a campground where we on staff all had walkie talkies we had to keep on at all times just in case of emergency. I noticed that every time I was inside the trailer and the receive channel on my walkie talkie picked up a signal, or I pressed transmit, the GFCI would kick out. When we packed up to leave, I found out why: the ground on the camp pedestal was bad and had burned my plug. It was necessary to replace the plug on my end, as well as the receptical on the pedestal. So, yeah, I suspect you have a bad ground somewhere.