More than likely most of the screws for the house portion of the RV are #2 Robertson (square drive) screws. Get a decent mating screwdriver; you won't be able to do much of anything without one. This was the first tool I got for my motorhome, and quite possibly the most used one of all.
A simple multimeter and an electrical terminal crimper are very useful for the electrical system.
It probably goes without saying, but a tire pressure gauge is rather essential.
I would think a 3/8 socket set would be adequate for most any repair I would care to attempt on the road except for changing a flat out—for which a decently sized breaker bar is useful. (I'm referring, of course, to a purpose-built breaker boar, rather than a pipe or something slipped over a ratchet handle....) For that matter, a couple of adjustable wrenches would probably suffice for most things, though they aren't as convenient to use.