What you are talking about sounds like SWAY (Side to side rocking like fans swying side to side at a rock concert) there are sway bars on your chassis, but... UPGRADES are possible in this area. Any RV suspension specialist can outfit you with better ones.
End of important response... Continuing to things you may discover
WAG is where the body moves to the right or left over the axle.. Often the front end wags one way and the tail the other (Like a dog's tail wagging) this causes you to make adjustments since you precive it as the motor home turning.. TRACK BARS also called pan hard bars. LOCK the body centered over the axle.. Stopping this 100%
Finally there are stabilizers.. These devices either try to hold the steering straight ahead or "Assist" you in getting there.. TWO of them (At least) are now adjustable from the driver's seat (you can re-center from inside) Blue Ox True Center and I think the other one is Saf-T-Steer. This may or may not make driving more relaxing.. I know it does on my rig.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times