First, if you do not have a rear track bar/pan hard bar, either make on, or buy one. The springs are 42" long, with large rubber bushing, and the MH has a large amount of force on the rear end. Wind, either natural or from passing vehicles, cause the MH to flex on the rear suspension, causing the sway, or tale waging the dog feeling. Then the CHF, or moving the sway bar ends to the inner hole, for more side to side roll resistance. From here, you can go as far as you like, can afford, with little improvements.
When we first got out MH, it was new, and I was chasing it all over the road, with very few exceptions. I could not find out what was wrong until I was taking to the dealer for warranty work with the wife following me. When we got there, she said the people were afraid to pass me because the rear end was kind of doing a sideways figure eight. When we got it home, I would push on the rear side of the MH as hard and I could to get to move back and forth in rhythm, and looked as best as I could at the rear suspension and saw a lot of movement of the springs under the chassis.