You'll want your Hopper 3 connected to your main TV with a HDMI cable, and you'll want to get to the point where you see the Hopper 3 output on your TV.
You'll want your Hopper 3 SatTV coax jack connected to the coax coming from your Trav'ler, you want the coax that is connected to the "C" port if there's more than one. If you had the Trav'ler installer set your RV up for a wired Joey 2 receiver on a 2nd TV then you may have a Hybrid Solo Hub (little box with bright orange sticker) in line between the Trav'ler and the Hopper 3.
Here's an image of one TV with Hopper 3 and multiple TV with Hopper 3 and a Coax fed Joey 2 or Joey 4K. This image is accurate ONLY for the new version of the Trav'ler that has the DPH LNB , which you stated you have ...
I'm guessing that if your sticks and bricks location you are moving the Hopper 3 from is in Avon Park Florida then it uses Eastern Arc there. The dish on top of your RV in multi-sat mode uses Western Arc and likely shows 110* 119* 129* on the control box when you power up the dish and it completes search.
When moving back and forth between S&B and RV you'll have to update your Hopper 3 as follows:
Go to Dish Diagnostics and go to Dish (press 3 on remote) Screen and select Test Installation (press 5 on remote). You'll get a Check Switch Status Progress box. If all goes well in the RV if the control box shows 110* 119* 129* Check Switch should find those 3 sats and show those 3 sats with green checks. You'll also have to do test installation when you move the Hopper back to your S&B.
You may lose your local channels if your local S&B market is not also broadcast on the western arc sats, or you are too far away from your home S&B location. You may have to give Dish a different address that will map to a local market that can be received on Western Arc. You can do this over the phone or via chat - just tell them you need to change your service address.
To find a local market that will work on Western Arc here's a map: