Good advice above!
Guessing at what cord is OK is a fun online game. Big cords, little cords, big plugs, little plugs. It all boils down the the voltage inside the RV. Get a voltmeter. Read the voltage inside the RV while something big is running. An accurate digital voltmeter cost about $15 at your local hardware store.
The best test is to run the A/C, but that is not working. So run the microwave with a cup of water in it. Measure the voltage. Run an electric heater or electric coffee pot.
AC motors will try to run at a constant speed. The lower the voltage applied the more current the motor draws. The more current, the higher the motor heat.
Many A/C's need a minimum of 108 volts. So you want 110 for a little margin. 120 would be better, but 110 is OK to run.
If the voltage is good, next check for hot plugs and sockets. Overloaded or defective plugs and sockets will get hot. Just use your hand. High temperature is bad if it causes melting, burning, smoke or flames.
A 12 gauge cord is OK if the A/C is less than 50 feet of cord and house wire from the service entrance. Use 10 gauge for up to 100 feet.
I wish you good luck and happy trails ahead!