Yes I have one car (1 of 4) that does drive wobbly like that, admittedly not quite as bad as yours. Looks like a poor setup or defective sensor feedback to me. It is very annoying at low speeds, when I added barriers and was able to race much faster the problem was less of an irritation.
If support can't help you then maybe try to pick up a cheap second hand set with at least one working AI car or some newer HW versions at http://hotwheels.mattel.com/shop/en-us/hw/advanced-play
Just had a quick search:
New Real Fx Colbalt Blue Car ~$20 on ebay.com
New HotWheels AI starter kit ~$40 Amazon.com
New Real Fx starter kit £30 delivered UK ebay.co.uk