the 1st thing to check is are the tyre pressures up the recommended maximum shown on the door pillar sticker.
also do you have the same make of tyre from left to right. If these are both OK then I'd take the car to a place that does 4 wheel suspension alignment, most places use the back wheels as a datum and assume that they are perfectly straight and true. Often this is not the case and many modern cars are now adjustable at the rear as well as the front. A 4 wheel alignment measures all four wheels independently and each is set -up without referring to each other. Let me know how you get on
normal driving with this car is excellant.it haa four new tires and the car has 38000 miles.as described the car sways back and forth dangerously from side to side as if there where a weak componet somewhere in the suspension system componenants when wind gusts push on the sides of the car.this effect is so pronounced that it alarms people driving in the carr.i agree that your answer outlines a reasonable check list however it does not get at the root of the cause.can you dig a bit more on the issue?
Now with the car jacked up on that side with the wheel about 2 inches off the ground use a steel bar under the wheel and lever the wheel up and down slightly, you should be able to look at the end of the axle and see if the suspension arm is moving up and down separately to the axle.If so replace the bush
To feel if there's a worn strut top bearing then lightly hold the spring by hand and have your assistant move the steering from left to right with the wheel on the ground - a worn bearing will feel 'notchy' through the spring. The wheel needs to be on the ground for the test to load up the bearing
while your response makes sense i cannot believe a car like this one should should already have such pronou ced wear at the low milage of 36000 miles.does this make sense to you in this context?