Another thing to be aware of is an AC unit typically draws about 60 amps during the momentary starup. When using small gauge wire like #12 and runs like 30', you can have significant voltage drop that is hard on the motor windings and eventually lead to premature AC unit failure. The 60 amps is also in addition to anything else operating like say the converter/charger at perhaps 4-5 amps.
I would use a #10 shore power cord with 30 to 15 amp adapter, or a #10 extension cord in addition to the shore power cord. As mentioned, you also need to consider the length of the branch circuit from the house's panel to the 20 amp receptacle which can greatly increase voltage drop.
Always have a permanent voltmeter mounted inside an RV and keep an eye on it. If it gets down to 104-105 volts, shut the AC unit off as it will cause damage. Best thing is an EMS which automatically shuts you down on low voltage. Also, always ensure the blades on your cords are kept clean and shiny and never plug in the RV with power on.
