Yes, you could take the Hopper & Joey from your home with you on the road. The Dish installer may not be willng to set up your RV installation though, but independent Dish dealers often will. You'll need to duplicate the home dish setup for your Trav'ler to use the Hopper 3, but that may be as easy as adding a Dish DPH42 switch to convert the Trav'ler LNB. You'll also need a Dish Solo Hub if you bring the Joey along. A Hopper 2 would only need a Dish Solo Node.
The Dish local channels are transmitted to relatively small geographical areas using "spot beam" antennas, meaning you'll lose them once you travel typically 100-300 miles from home, depending on just where your home is located in the spot beam pattern. To get the locals in you new location, you just call or chat online with Dish Customer Service and ask them to change your "service address", but not your "billing address", to the new location. In a few minutes, your program guide will update with the new local channels. There is no limit on how often you can change the service address. I do it daily at times, and have even done it twice in one day with no problems. Dish does offer a "distant network service" that allows you to receive the LA local channels nationwide, but you would lose your locals when at home.