I have the Winegard Traveler SK-3005 automatic roof top dish on my coach. If you tell the RV park where your dish is mounted on your RV, 90% of the time you will have no problem with reception. The rain hitting the dish problem is the same as it is with your dish at your stick built home. Usually not much of an issue.
The dish is something that you can install yourself. The only hard part is getting it up on the roof. The dish itself is exactly the same size as the dish that you have on your stick house. There are connections on the dish to run coax to four different TV's from the antenna and you can watch different channels if you take two boxes with you. You probably already have a roof penetration point on the coach that will allow you to fish the coax down from the roof. The Winegard Traveler and antenna has HD capability so you will get more channels than the SD dishes with your DirecTV account. Some channels are only broadcast in HD and if you want to watch them, you have to have an HD Dish.
We use our crank up antenna for the local network channels and have no problem finding them with our King Jack antenna. Most of these are broadcast in HD and the King antenna has the amplifier built in to the antenna.