Final update on this issue (I'm the one who started this post):
Thank you all for your response posts and suggestions. By and large, you were all spot-on. After having Goshen Hyundai diagnose the problem, I took my car to a local reputable tire place. The employee told me that the manufacturer's warranty would not cover anything in my case, as the problem (cupping) stems from poor alignment and a lack of balance and rotation, not as a result of a defect in the tires themselves.
I then made an appointment with Glenbrook Hyundai, the dealership that sold me the car. To make a long story short, the service manager drove my car by himself and then told me he didn't notice either of the problems I stated (a pull to the right and shaking/shimmying at high speeds). He then offered to go for a ride in my car with me driving, which we did. I showed him how the car continuously pulled to the right every time I let go of the steering
wheel even on a flat street, and he said that the pulling was "normal." Afterward, he sent me around the corner to an affiliate dealership to have them check my alignment. After ten minutes, the technician came out with a printout that said "Alignment Diagnosis: FAILED." I went back to Glenbrook Hyundai, showed the service manager the printout, and he said "Huh" and "I'll take care of that right now." They then performed an alignment for free, after which I drove the car, and it drove perfect. No more pulling to the right.
With respect to the two badly cupped front tires, they told me that replacing them during the CPO inspection process was not required by Hyundai as the tires were not damaged or unsafe. They were admittedly aware of the uneven wear, but did not conclude that replacing the tires was necessary. They quoted me $575 for two new tires, mounting, and balancing. After speaking with the lead sales manager, I was then offered two new tires for $300 even (no tax on top of that) where the sales department would eat everything above $300. I said yes, paid the $300, and have two brand new, non-cupped front tires. My car now rides much better and there is no shaking or shimmying at high speeds.
Was I happy about paying $300? Of course not. But was I pleased that the sales department was willing to cover approximately half of the cost as a result of my complaint? Yes. Some of you may say, "I would have thrown a fit and demanded they replace them for free," while others will say, "See, I told you to expect to chip in some money!" I'm just glad this issue is over. And I won't be doing anymore business with Glenbrook Hyundai. If I didn't mention it before, their 150 point certification checklist said my fog lights and fluids were in good working order. Well, after I bought the car, I found out both fog lights were blown and the car was almost 1,000 miles overdue for an oil change (they ultimately fixed both of those for free). I also found out well after the purchase that all CPO Hyundais come with a 90 day free period of satellite radio. I was never even offered or told about that during the purchasing process. Whatever. My admitted nit-pickiness aside, I'm movin' on.....
