Steering can feel light and floaty after getting new tires, but that goes away as the new tire surface wears in, within a few hundred miles. This problem has continued throughout the life of the first set of tires so the cause must be something else. Was the dealer who checked the car the one you purchased it from, if so how motivated were they to find a problem? Similarly, dealerships and franchises aren't the best places to find technicians with the skills or interest to dig more deeply into handling and alignment problems. Here's how you might proceed:
- Establish a baseline, drive HL's of the same year and model to see if the problem is common to the type or unique to your vehicle.
- Does your car have the OEM wheels, or at least wheels with proper diameter, width and offsets? As previously mentioned, check for proper inflation.
- If it's just your car, locate a suspension/alignment specialist who can check whether the body has been distorted, such as in an accident. If this is the case and wasn't disclosed pre-sale, you might have a strong case for a refund or at least thorough repair. Otherwise make a decision on having it straightened vs. dumping it. A reputable body shop (they exist) can perform the measurements and, if necessary, recommend a competent frame specialist. However, I'm familiar with cases where even after a body was returned to spec. it still didn't handle properly, one tire would wear unevenly, etc.
- Assuming the body meets spec., seek out an independent suspension/alignment specialist to give you car a thorough going over for worn or damaged parts, and if any, fix those before moving on to alignment. You'll probably need to search for the right place - you might ask an independent mechanic, the local high school or community college auto shop instructor or local track racers or car clubs. Bad struts/shocks can create a floating feel but might not be obvious from a physical inspection, and worn bushings can cause subtle issues.
- Sometimes the standard alignment specs won't work for a particular car, but a truly knowledgable alignment specialist can tweak individual adjustments to solve a handling issue.
Best wishes.