We would never leave the gen running while away that long. Nothing to do with dogs. IMO too many things could happen where it quit, breaker pops, who knows? Might be different with a MH and an installed gen, no idea.
If you don't like to leave the truck running with the air on while you are away from it, in a restaurant say, perhaps some of those places have enough parking you could take the rig itself. Now you could nip out and check on things often enough the dog will be ok.
Back to the campground afterwards.
Some places might have a dog-sitting service you can use.
