The OP *DOESN'T* have DirecTV (DTV) today. JHilley is recommending installing DTV in the house and then taking a receiver with them in the motorhome. Then the OP will be back to complain they don't receive local channels once they leave their local spot beam.
My approach is to install DTV in the motorhome first. Then move some receivers from the motorhome to the house. The RV account is eligible for DNS so the OP will always have network stations (on the motorhome and home receivers) regardless of where they are.
The issue of a dome antenna vs a Traveler is really a question of wanting HD service or not.
Legally, DTV wants you to have two accounts - one for the home and another for the RV. Taking a receiver from the home with you in the motorhome is not supported.