I don't think the receptacle is your problem. The tester would show you if you have a problem there.
Do you ever get a slight shock when you touch any metal on the trailer while standing on the ground?
Have you tried putting that AC tester in all of the receptacles in the trailer?
My dad's friend had a trailer with similar issues, and it turned out to be an extension cord wired wrong they were using at home. The indicator was that their problem went away while camping. Didn't use the cord while camping.
I had a 400hz converter I worked on in the Navy that started acting strange. It turned out to be corrosion on a ground for a circuit card. You could test AC between the circuit ground and equipment ground. Cleaned that ground and all was good.
Sorry just rambling, trying to throw out ideas/past experiences.
Please let us know when you find the problem.