JRT's are awesome dogs but very high energy, as you said. We had one that we had to put down several years ago. This was before we got into RVing, so not sure how he would have reacted to it. We do have 2 terriers now that we always take with us, and they do pretty well.
We follow the same routine in the RV as at home. When our younger dog was still kept in a crate, she stayed in a crate in the RV. She's older now and has free roam of our bedroom when we leave the house, so we leave her out in the RV now as well. We leave the radio on talk radio when we leave for background noise. I think it helps keep down the barking. They don't bark incessantly but will if they hear another dog barking nearby.
We also walk / run with the dogs in the morning if we're going to leave for a while to try to tire them out. However, having had a JRT, that might help a little but ultimately their personality is their personality, no matter how much you exercise them. What I mean is, if the JRT is a barker, he's going to be a barker regardless of how much you try to tire him out. I could NOT tire mine out. I'm a marathon runner and I'd take my JRT for 1+ hour jogs and he wouldn't get tired unless it was 90+ degrees and sunny. I remember many times taking him for long runs, then taking him to a dog park to run around. When we would get home, he'd look at me like "okay so now what are we going to do?" Don't get me wrong - he wasn't destructive and was pretty calm inside the house. But I rarely could tire him out.
Ultimately, the only way to know for sure how your dog will react is to try it out, as you said. Have fun with him, and he will calm down as he gets older.