Just because you have a Genie in your house does not mean that you could not also have a standard receiver like an H24 or a DVR like the HR24. You could then take the Genie and the babysitter would still have satellite TV or you could take the H(R)24 with you and leave the Genie at home. Just depends upon who wants what.
As mentioned, the receiver in the RV will get the same channels at home and this includes the Network channels. So, once you move a few hundred miles (more or less) you will lose ALL Network programming (ABC, NBC, etc.). You can call in and have DirecTV change your service location to where the RV is located but doing so will effect all receivers on the account so your home receiver will stop receiving ALL Network programming.
If one of you has an OTA TV antenna you can use that for the local Network programming and you don't have to call anyone to do anything as ALL of the other cable type programming will be available no matter where you park the RV.
What I post is my 2 cents and nothing more. Please don't read anything into my post that's not there. If you disagree, that's OK.
Can't we all just get along?