Buy an inexpensive digital volt meter and measure the voltage you are experiencing in the rig with the AC on, on a hot day. Harbor Freight, Wal Mart, Sears all have them for less than $15. With the load on, you should not have a voltage of much less than 110 volts. Down in the 105 volt range you start to have problems with both the AC itself and the load on the breakers (voltage goes down, current goes up).
You should check the temperature of the plug from the trailer where it goes into the panel at the campground. If it is hot, you have a high resistance and probably need a new plug end to your cord. Also the campground outlet itself may be loose and causing a problem.
You also can check for breakers which are warm or hot. If any are, especially the AC breaker, it may have either a loose wire connection or the breaker itself may have just become old and tired. I had a similar problem on one of my RV's and found the wire to the breaker had actually melted the insulation near the breaker, due to a loose connection.
If you are not comfortable with electrical issues and repairs, I urge you to have a professional look at it.