AC Voltage Through Frame/Stablizers

Go ahead and get a $5 outlet tester and use it.
Then try plugging into a GFI outlet and post the results.

You guaranteed have a grounding issue. If your using an adapter of some sort, that is the first place I would go. They are infamous for failing at the ground lug. Also check polarity of the receptacle your plugged into It is possible that it is wired back words or there is no ground there.

I have used the multi-meter to check the plug I use to connect the trailer to power. I can only get voltage through two connectors, which I believe is what I want. When I go into the breaker box, I was getting power between the black/white wires and black/ground (solid copper). I disconnected the ground from the incoming power wire and can still get power from the ground. I am wondering if one of the AC appliances is causing a problem, or the wiring to it is the issue.

Almost always a bad safety ground thru the green ground wire in your power cord. Could be a bad cord, a bad connector on the cord, a bad outlet. Start with the outlet and go from there.
If you don't have one, buy one of the small plug in ciruit testers available at your home improvement store.

It sounds like you may have a polarity problem. Check the wiring in whatever you are plugging into. Also check to make sure your cord is correct.