As a quick answer, and due to there not being any real specific data in your post, I'd say that the main reason for the "handling" of the car changing is due to an increase in the unsprung weight of the rims and tyres, possibly an increase in the rotational mass and changes to the track width and suspension geometries from the use of the wider rims.
As you haven't stated the type of car in question, then the fixes are hard to quantify for you.
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