My advice is to get "travel tags" for the cats. Have the cats wear a collar or harness all the time with the tags. The tags should have your cell number AND your RV license plate number - that way, if one does get out and someone finds them, it is very easy to get him back to you. I did that with my dogs - I used to use a barrel tag with a note inside on which I wrote my campsite number. Now, I put their travel collar with the tag on them and they can be reconnected to me via the plate number.
My other comment is that many cats can get startled and run. If the door is open, the cat may go out it even though they've never shown an interest in the outdoors before. The RV is a lot smaller than your home and the cat can't separate itself from scary noises, etc., as easily.
Definitely spend time in the RV at home before you start moving around with the cats. Let them get used to it stationary first. Then take short trips. ALWAYS have cat carriers for all three with you when you travel - you never know if you'll need to transport them elsewhere.
