Hi ace66,
Class C drives like a car. Class A drives like a truck. There is more side to side movement because there is a lot of weight going from side to side because of any imperfections in the road being flat. The chassis will follow the weight shift of the coach. If you are sure you are on a flat road and the coach drives like a dog hunting rabbits, consider:
1. Make sure all the suspension (front an rear) are in good working order and adjusted correctly.
2. Have the steer axle tires aligned.
3. There are quite few after market suspension products. Track bar (front and rear), shocks, steering stabilizer, etc.
4. Go to
RV & Truck Parts - Suspension – Steering – Brakes - Towing and take a look at some of the choices.
If you decide to get a steering stabilizer, I recommend the Blue Ox Tru-Center. Go to
Blue Ox TC35270 TruCenter Steering Stabilizer
None of this is cheap. However, I have installed quite a few after market suspension and steering products and am very pleased with the results.