I would also disagree with the long-gun suggestion, RVs are usually pretty tight quarters and a handgun will give you more maneuverability. If you do want a long-gun, stay with as short a barrel as you can. A short carbine (maybe a lever action) may be a good way to go if you want the long-gun.
This is one of the rare situations where a handgun is more tactical than practical. Not entirely, of course, but to a degree.
Absolutely, the handgun is easier to maneuver in tight spaces, (like inside your RV), no arguing that. BUT, is that the MOST important thing? Is that what you will need, most often???
My father in law did a lot of RV camping, and traveling in the US and Canada. While he had a couple of old shotguns, he was not a "shooter" or a gun person. Back in the later 80s I made up for all my sins in his eyes when I gave him a Marlin .357 carbine for Christmas.
He absolutely loved it. I'm not certain he ever actually shot it, (after the first time) but he loved it. The Marlin carbine in .357 is pretty short, holds 9 (10 .38s), and has very light recoil. .357 Mag is widely known to be an effective defense round.
Now, its true the carbine is more awkward in tight places than the handgun, BUT for him, that wasn't his main concern. What the carbine gave him was something that could live in the corner of the wardrobe of his camper, took up very little space, and WAS LEGAL nearly everywhere he went.
A handgun did not do that. The legal part. A lever action rifle (or pump, or other manually operated repeater) or shotgun is legal, without a permit in nearly every state. Back in the 80s, before the current levels of paranoia, you could even take them into Canada and return.
There are a couple (2 I can think of, there may be another one or two) states that require a permit for ANY gun (usually called an FOID -Firearm Owner ID card), and those should be allowed for in any travel plans. DO some research on ALL the states you are travelling to or through!!!!
There are several states that require permits for handguns, but do not for rifles and shotguns. AND by choosing a lever gun, or pump, or even a double barrel shotgun, you avoid all the laws about "assault weapons", which vary from state to state as well.
Short barrels (20") meet all the legal restrictions I know of (some places allow 18" some don't, 20" is allowed everywhere as far as I know), a folding stock MAY be practical, may, or may not be legal, depending on the state.
Avoid a semi auto long gun, detachable magazines, protruding pistol grip, (the whole "evil black gun /weapon of war" thing), and you will likely avoid all the legal entanglements they have in states with "assault weapon" laws.
There is nothing wrong with choosing a handgun and the handgun absolutely does have some advantages to its
use. But, the long gun provides legal advantages to TRAVEL that due to our various state laws, a handgun does not.
One VERY important thing to learn is the laws of ALL the states you are going to be in, or travel through. The 1986 FOPA act provides some legal protection if you unintentionally break a state's gun laws while travelling through, but it only applies in certain situations. Do some research, seriously, its important.
Good luck!
(nothing wrong with a good .357 revolver, other than the legal hassle of staying within each states laws as you travel)