Kardar2,
A weak or dirty receptacle can cause the plug to heat and cause a drop in voltage. Compare the voltage at the campground receptacle to voltage inside the camper at a receptacle. That sounds like what you are describing.
My rule of thumb, if the interior receptacle is less than 110V with the air condition running it may cause problems. (Measure with AC running)
If the air conditioner evaporator and/or condenser get dirty that can also increase the current drawn. I wash my AC every couple of years.
Every RV AC problem I've ever had was due to a dirty unit. (Sometimes dirt daubers)