Your problem appears to be the ungrounded cord. I would tell your dealer that, as, he may be looking for something that is not there. He can plug in a cord and if there is no problem then no repair. The trailer uses the frame as the neutral. In a house your neutral is grounded to ground, so no issues. Same with your trailer. Guess the lesson is, make sure your cord and receptacle are both grounded properly. It would be rare for a campground to not be properly grounded, as it would cause issues immediately.
2011 Toyota Tundra double cab