Chipfo,
You actually have two (2, duo) issues.
First as others have said is a bad ground and that can be in your rig or in the pedestal.
I would start at the pedestal. Pull your plug back enough to get a probe to the ground pin (the one that is not flat) and test between there and any metal on the pedestal. If you don't find anything at the pedestal, try sticking the other probe in the soil nearby.
Can't get the probe to the ground pin?? Wrap wire, a paper clip or something conductive and clean around the pin to you can get the probe on it. Aluminum foil works too, but it is not my favorite.
If the pedestal is bad, tell the management about and ask for another location.
If the pedestal is good, then your rig has two problems. You have both a bad ground bond and an ground someplace that needs to be fixed.
It is my experience that both problems can usually be located with a visual and mechanical inspection. (You said you opened all the breakers, so it is not likely to be a problem with installed equipment.)
With the shore power disconnected, use your meter on a resistance scale to check between the ground pin and the power pins of your coach plug. It should be no greater that what you see if you hold the points of the two test plugs in different hands.
If what you have related is accurate, the meter will probably move.
So, start opening things up and looking. Check the tightness of every (and I do mean EVERY) screw you can find and look for a wire that is loose or might have chafed.
Look at any conductors that are up against the main box. You will have to search, but you should be able to see the problem. I have found more than a few of these, and all but one was visible to the naked eye. The bed ones were caused by forest friends eating the cables.
Matt