I would have DirecTV add another receiver to your home setup. Any of their receivers will work. If you want to be able to take a DVR into the RV then be sure they set you up with an HR24 and if you don't want a DVR then have them install the H25 (tiny) receiver. This receiver does require the DirecTV SWM setup but you are going to want to use that with your tripod setup in any case to make the setup and installation the easiest. When you buy an antenna just be sure they provide a SWM3 LNB and the 21V power inserter.
I assume you know you could also simply move your Genie between the house and the RV is you don't want to pay for an additional receiver plus the additional monthly charges.
For the antenna/tripod setup a number of RVers use the equipment from this supplier (I have no connection to them).
TV4RV