"gshantz"....I had the same problem years ago on a Class C Jamboree that I owned. It originally came with Michellin tires. It ALWAYS handled well, but eventually needed tires. I went to America's Tire Company for the purchase. I was in my late 30's with a family and needed something less expensive than Michellins. America's Tire Co. made me a good deal on Kelly Springfield tires, which are a sub brand of Good Year.
A few weeks after installing the tires we left on our yearly boating trip about 400 miles away and a trip we had made a dozen times in the motor home. Five or six times during the trip we traversed some large sweeping curves and "S" curves on HWY 99 in California. On all of the curves, at highway speeds, the motor home felt like it was "rolling" right off of the tires. It did EXACTLY what you described. As you made the turn, the chassis was following the turn, but it felt like the coach would take a second or two to come around in the direction of the turn. This was a very uneasy feeling.
I knew exactly what the issue was.....the sidewalls were not stiff enough to keep the motor home from having the rolling effect. The Kelly Springfield tires were the same weight and load rating.....they just didn't work on my setup. When we returned from the trip, I paid the additional money to put new Michellins on, like I had before. Problem solved.
You need to change to something else. Demand the that the tire store, for safety reasons, move you into another tire. Since you didn't have the issue with the Michellins, I would bite the bullet and pay the difference.