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This is not normal and uncommon.
The first thing I would do is talk to the dealership. Since the vehicle is new it should be fully covered under the manufacture warranty. If there is a problem with one of the tires it will cause all of the problems you are currently having. You cannot always see the issue with the tires but I have seen a few with too much air, broken belt on the inside of the tire. Also if they have special tires with arrows normally on low profile tires if the arrows are going the incorrect direction it will be a issue.
But like I stated in the beginning there should be absolutely no stability problems wondering ect. Unless there are headwinds causing it to wonder that is the only thing that can happen. But if not get it in immediately before one of the tires wears down much sooner which can cause major problems like a blow out.