Hi JeremyN,
Your situation might be simply a bad GFCI in the park pedestal, but the other possibilities need to seriously concern you. Having voltages present on the (hot skin) chassis of your rig is a potentially fatal condition.
My first advice is that I would have the CG test their circuit/GFCI and move you to another site.
Barring that, I would open your main breakers and all circuit breakers in your coach. Assuming the GFI holds and does not trip, you should check to see if you have any power on the frame of your coach. A decent a non-contact voltage tester works best for this. I would close your coach main breakers and then your circuit breakers one at a time, with someone testing for voltage before closing each consecutive circuit. When you close one of your circuit breakers, I would expect one of them will trip the GFCI. Then you will have identified the circuit with the ground fault.
Be safe and keep us posted as you learn more.