Ron,
I think you might start out with reading about your EMS and how it operates. What is unclear is if it is responding as it should. For instance, even though you had a light load on your coach shedding started, but the camp ground circuit you were on could have had a heavy load elsewhere and voltage on your pedestal might have been low at the time. When shedding occurs you need to measure and see if the EMS is acting according to spec for voltage and current or not. Start up current on air units can be significant and can cause momentary high currents which can cause issues.
As far as black copper, there should be no signs of excessive heat or any issues like that. If there is then I would change the wire out. Heat means voltage drop and possible fire hazard. If it was night time with no sun involvement and you placed as heavy a load on the circuit as you can (2 airs, water heater element, toaster, hair dryer, whatever it would take) and you measured the heating of the cable after from end to end with an IR gun you would have some idea how much heating is taking place and if the ends have absorbed moisture or blackened and the heating is primarily there or uniformly along the whole cable. The copper itself could have been contaminated and it is a uniform issue or perhaps just the ends. It may take a bit of time under load, given the rubber covering insulation, to sense the highest level of heating by IR gun. You may have to repeat a similar high load test on a friends coach to compare cable heating and interpret the results if it is not obvious. If you had heating end to end uniformly that issue would probably need a known good cable result to compare to.
Last but not least, the contacts on the plug should be bright and shiny and push into the outlet with some physical resistance. That location can heat significantly due to poor contacts. I watched a 37 ft fiberglass boat go up in flames due to heating of the plug due to resistance issues.
Later Ed