We had an older Class C, about the size of yours, on a Ford E350. Rebuilding the front sway bar with new end links and end bushings, made a big difference in the coach's stability. I replaced rubber with polyurethane.
I helped an OP here on RV.net with installing a Hellwig rear sway bar on a Chevy chassis and he noted a big difference. Even more importantly, his WIFE noted a big difference...
EDIT: From the pic, it doesn't look like the rig is riding low in the rear, but it's certainly possible that the rear leaf springs have gone soft. An RV isn't like a box truck. RV is pretty much fully loaded all the time. That's a lot of weight standing on the springs, 24x7, the whole life of the RV.