The shaky sections are beyond use imho. It's easy to rig car mounts without huge expense, even a tripod with a still camera style pan/tilt head poking out of a window, with the legs extended inside and held by the operator braced out as much as possible will give you a steady mount clear of the camera car, or in this example I simply used multiple ratchet straps to cobble a whole tripod on to the outside of a van (safety has to be thought of here)
Watch the second half in the higher quality version
I agree some info on the car would help, along with some more dynamic shots. Try filming it from as far away as your zoom will allow, this compresses the perspective and gives a vehicle a more solid robust look, also push those low angles more if you can, gives the car a domineering look. I'd also choose light from either end of the day, early morning is best, again visually more dynamic.