Did you get proof that your new-to-you King Dome system is in good working condition? If not, you may be in for a nightmare.
I bought my StarTrac SV360 in-motion system back when I bought my 2003 Dutch Star. It worked flawlessly up until 2 months ago, and I'm still trying to figure out exactly which of several TracStar "boxes" I need to replace.
BTW I've eliminated the DirecTV receiver from being the problem, it still works fine.
To answer your question, according to DirecTV, there's two ways you can do it. IF you already have DirecTV in your house, they can lease you a small receiver for your RV, cost is $5 per month for this receiver. There are other caveats. If you only want to subscribe for your motorhome, I believe you have to be a fulltimer (live in it all the time).
I don't know about the other vendors.