We get better than 8 mpg, more like 12, but we have a truck/trailer, not a motorhome. My husband keeps saying a motorhome would be easier to back up. We've also heard that two axles are easier to back up than one axle.
Our trailer is 16', so probaby not big enough for your needs. It's just right for 2 adults and a golden. Once we are in the trailer, Casper thinks it's a giant crate, and adjusts his activity to match. He sleeps in a crate at home. In the trailer, we make up the dinnette cushions into his bed at night. He sleeps there until the second we roll over in the morning and then he tries to jump on the bed. Sometimes he succeeds.
One of the best things about the trailer is that it is familiar to the dog no matter where we go. At the end of the day, no matter how we've messed with his schedule, he falls right back into his routine at the trailer.
A/C and heat depend on where you live. We live in Western Washington and are glad we have both in the trailer. Eastern Washington is pretty hot! The heater is not quite strong enough to keep the place toasty, and it's really noisy. Really, really noisy.
Also investigate what power is available at the dog shows. I've read that group events like that only supply a minimal amount of power, not enough to run things like the AC, heater, frig, TV, hair dryer, etc. For that, you'll need to carry a generator big enough for the job, and you'll need to be aware of what hours you can run the generator.
We just got our trailer this summer, when Casper was a year old. We're having a lot of fun with it. It is a bunch of work. It needs the same maintenance as a house (it has all the same systems). Not sure where you live, but if you live in a cold climate, you have to winterize it.
If you have a lot of gear, check around for how much storage you get. I got the small trailer to keep things simple. I don't want to spend the weekend with a bunch of stuff. We went on vacation to California for 17 days in the trailer thus summer. I didn't feel crowded or that I was missing anything at all. And when the dog got so, so sick, it was nice to have a familiar retreat.
Doggie specifics. Casper has his own drawer of stuff. He sleeps on the dinnette. He brings in a lot of dirt. The floor of the trailer is really, really cold, even for a golden. I wish we had a stronger screen door. Casper hasn't tried to crash it open, but it would be trivially easy if he ever tried.
There are forums for RVs, too.