So we took our first mini-trip this past weekend on the coach and had an absolute BLAST!! Everything worked great and we couldn't have enjoyed ourselves more unless someone else paid for everything! ...
The first thing I would check is the rear sway bar bushings. Ours had completely rotted away. Once I replaced them it was a huge difference. Then I added new shocks and the combination of the two has made driving much more enjoyable.
To answer your question.... No, there should be no significant load on your sway bar if it is sitting level and on a level surface. No need to jack the coach or axles up.