At the risk of repeating someone.
A 13,500 BTU AC "CAN" run on a 2000 watt generator, IF YOU HAVE AN EASY START capacitor start assist.
https://www.amazon.com/SPP6-Capacito.../dp/B0002YTLFE
This giant capacitor is like a battery in that it stores a bit of energy that it can dump at a high rate for a short time. Just enough to launch the compressor motor. Once running, the compressor requires substantially less power, so nominal 2000 watt peak/1600 watt continuous generator can just barely run it.
It turns out that your home shore power can meet this minimal standard if nothing else is loading the circuit and your circuit breakers are not tired. Ideally your circuit will be a 20 amp circuit, but a 1600 watt genny is only delivering a bit more than 13 amps.
You CANNOT do this with a 15,000 BTU AC, but with a soft start and a 20 amp circuit and a #10 AWG lead cord as short as possible, you MIGHT get away with it...so long as you add no other loads to the circuit - in the home or in the RV.
As others have said, if this is important to you, install a 30 amp circuit. If your main panel has an open spot, install a 50 amp breaker. Feed a sub-panel like this one with appropriate wire for the distance needed...typically #6 AWG. There are many variables in this equation depending on how your main panel is installed, but you could run the feed wire in conduit around the outside of your foundation/sill plate. You could even bury the wire in conduit and run it to a 6" x 6" post next to the RV parking site, and mount the box on that post. (the Siemens box is meant for outside use.) I'd recommend against direct bury wire. Unless you are in ideal soils, rocks and other debris can wreck direct bury wire. Use conduit if you go in the ground...no matter what code allows.
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
You're starting to talk real money in some situations, but if you park next to your garage, and if your garage is already wired with about 50 amps, you may be in luck...especially if there is a sub-panel in the garage. Like I said, many variables.
I just installed this box at my home. I'm very pleased with it.