DirecTV will not be able to help you with anything RV related. Your best source of information will be here. You have been given several good ideas so please let us know where you are still confused or how we might clarify something.
Your basic question was answered in that you cannot use the Client (C31/41) as a stand alone device. They must be connected to the same antenna/cabling as a Genie. You can, however, take your Genie instead (or in addition to) and use that in your RV. Now you have the benefit of a DVR plus the ability to watch different channels on different TV's.
It's only the antenna equipment required that makes this movement a slight issue but it is very, very easy to deal with. You either add a kit to your current setup and it all works but you don't get any of the programming in HD (same programming, just in SD) or you buy a separate antenna to use when you are in the RV. This could be a roof mounted automatic like the Winegard Trav'ler or a ground home style antenna on a tripod which you point in a very similar manner to your current 18" dish.