Given that info, if you're absolutely going to stick with a single generator, I'd go with the Yamaha EF2800i. One EU2000 would be on the ragged edge even at sea level, and I'm afraid it wouldn't be long before you're seeing blue smoke from worn piston rings.
At its rated output at sea level, the EF2800i meets the minimum requirement established by Duo-Therm for your air-conditioner, and it should still be able to provide that up minimum power up to about 3,000' ASL.
It weighs a LOT less than the electric-start 3000W models from Honda and Yamaha.
With 3.0 gallons of fuel vs 1.1, it will run about 2.7 times longer between refills than an EU2000.
It's blue, like the Airstream awnings (unless they're burgundy like the Limiteds).
It's a lot heavier than the EU2000, especially when fueled (about 85 lbs). Try to make sure it's as empty as possible before having to load or unload it.
It's more awkward to carry. You have to carry it in front of you with two hands. Better yet, have two people to lift and carry it.
The gas cap is vented and doesn't have a shut off like the Hondas. Again, make sure the fuel level is low if you have to tip it.
Even operating at less than rated capacity, it's going to be 6-7 db louder than a single EU2000 working its heart out. Put the Yamaha about 2.2 times as far from the trailer as you would the Honda and that will make it about the same sound level.
If you decide you want to be more of an electricity hog, or camp at high altitudes during hot weather, in the future, you'll have to replace it. It can't be paralleled with another.
Yamaha makes quality equipment. As long as you keep power usage limited to the AC (and that means holding off on AC until the batteries are charged if you use a significant amount of DC the night before), the EF2800i should be adequate.
I might also mention here that the preeminent on-line vendor of Honda generators, Mayberry's, no longer sells Honda equipment, since Honda started hammering on-line vendors with quotas and advertising restrictions. They've switched to Yamaha. There are hundreds of RVers who've been happy with Mayberrys' service and I'd recommend them as a source for the EF2800i.