[WDPatterson]

I have been living off grid with my wife, since late 2017. I started out using a champion 100222, which put out 4000-watt speak, and 3500 Watts full runtime. It barely kept up, because we ran the 15KBTU air conditioner AND the ice maker. If we wanted to run the water heater on electric, we had to turn off the AC. If we wanted to run the microwave, we had to turn off the AC.
In late 2018, I upgraded to the model 100216, which is 4500 W Peak, 3650 Watts run time. That one, of which I now own (6) each, outputs enough energy all day and all night long to run the air conditioner, the ice maker, teo TV's, and barely run the microwave... I say "barely" run, because it bogs down the generator too much. So, still better to turn off the AC while you use the microwave or the water heater.
Living off-grid gives us some advantages. We have put up a rack with (12) 370w PERC-72 PV panels, running through a Midnite Solar Classic 200 charge controller, into 200 amp hours of 48-volt prismatic lithium iron phosphate rack-mounted pods. These are smart pods, and they output through a 5000 watt AIMS inverter. So, we are getting everything we need, during the day.
Before I assembled the solar system, I was running generators day and night, one at a time. That means I ran that generator for days on end, just keeping it fed with gasoline, only stopping it to change the oil every hundred hours. They don't last a real long time without proper maintenance. However, they'll get the job done.
At one point, I had a generator failure which required me to borrow a generator from my son-in-law. His was a 6500-watt roll-around generator, which was ridiculously heavy. However, you could run everything in the trailer off of a 110 volt socket with a 20 amp breaker.

The funny thing about most generators is they run so much wattage, but each outlet is still rated very much like a home system. Standard 120 volt, 3 prong connectors are rated at 20 amps. The 30 amp RV connector, which you find on most trailers and fifth wheels still has a 20 amp breaker, but will run 30 amps. In fact, we often run the entire RV from the RV connector on the generator. Never had a problem with those connectors.
I recommend the champion open-frame 4500 / 3650 Watt generator, because it actually has the 30 amp RV connector on it. It also has a selector for 120v and 240v connections, using a locking 4-prong connector.. I highly recommend this model, because it's one of the most portable, it's easy to grab onto with its open frame, it's easy to pull maintenance on, and it runs all day and all night. And, yes, you can get a wheel kit for it.

I would emphasize this caveat:
Put everything in the shade, if you can. Make sure you shut it down and perform oil changes every hundred hours. Get yourself a small fan to push air across it, that way it'll stay cool even when there is no Breeze.

You can go to Tractor Supply, pick up this generator for less than $400, and it will serve you well for at least a year. Champion's warranty for defects and workmanship is 3 years, their online support is 5 years. DO NOT by the Tractor Supply warranty. It will do you no good. Owning six of these, I talk to Champion support, periodically. They have treated me well, have answered my questions well, and I trust them.
Knowing that you have dogs that you leave at home, I would recommend that you set the thermostat at like 78 to 80 degrees, while you are gone.
Air conditioners are only capable of creating a temperature differential, and there's no good reason to overwork them. By all means, put that travel trailer in the shade. Put a tent over the generator. And run a fan on that generator.
Hope this helps, and good luck!!