Actually you need to check the voltage inside the RV while the A/C is on. If it will not start, and you want to find out the voltage, plug in a electric heater to put a 15 amp load on the electrical system, and determine the voltage.
My guess? You might have a bad run capacitor.
You might have a bad electrical connection, or the plug might not be gripping the RV cord tightly.
I was in a RV park once on a hot day, and found I was only getting 108 volts. So I went to unplug and put in my 12 volt booster, but the plug was very hot - like a toaster. I was getting a 10 volt drop across the plug, and at 15 amps, that is 150 watts drop across the defective cord plug.
SO you have a few things to check out, google bad popped capacitor.
Find out your voltage at any receptacle in the RV while there is a 15 amp load on the RV.
Good luck,
Fred.