Advice on driving stability - Fleetwood Southwind

If, when you say it "sways", does the body rock back and forth sideways, or is it difficult to keep going in a straight line on the highway?

If it rocks, get your sway bars checked. If its the hard to steer, make sure the front end alignment, especially the caster, is correct. Weigh the coach as loaded for travel, and set the tire pressure per the tire mfg's recommendations. Install a trac bar on each axle.