OP - sadly, many cars will drive the way you describe because of the type of tires and suspension they have and the types of roads they get driven on. Some vehicles with a mushy suspension and soft tires are somewhat non-responsive when driving and could account for the delayed response and/or swaying - in other cases, some tires have developed reputations for following ruts in the road. One option is to try a different set to see if this alleviates the problem. Yes, it will run you somewhere around $400+, but that's a small price to pay considering the alternative.
Jeremy - DARCARS is one of the shadiest dealerships in the area (frame damaged, Frankensteined weld-jobs, entire car resprays, etc), but I don't think you can entirely hold their salesperson responsible for your licensing and titling issue. While I don't know the reason for you having a TN license while living in PA, most states require you to get a valid state issued license within a set time period - exceptions usually being military personnel and college students.
In some cases, the onus is upon the consumer to determine what steps they should take to register and title a vehicle, because out of state dealerships are not experts in local motor vehicle regulations.