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The air has no reason to change it's relative position? Why not? Is air immune to interia? Why?
The fact of the matter is that the air is "pushed" towards the back of the car just like anything else (air is a thing, you know) in the car. You just don't notice because air pressure is about 100KPa, which is significantly more than the extra pressure caused by the accelerating car (easily much less than even a single Pascal). Believe me, if you were to put that air in a centrifuge and spin it fast enough, there would be a vacuum towards the center of spin!
Also, if you think that the fly has approximately the same density as air then you've never swatted a fly in mid-air. It falls quite quickly (although it's terminal velocity is quite slow). If you want to see something with the same density as air, try a poorly inflated helium baloon.
If there were no windshields, the car will most certainly drive away from the fly. The fly doesn't drive along with the car simply because it's in the car, or because the car is sealing it, or that there is air in the sealed car. It's because something pushed it, either it pushed itself (by flying in the direction of the car) or because the back windsheld pushed it forward. As I've said before, the air in the car will have pushed it forward a little bit as the fly approached the back windshield but, because air friction is exactly that--friction, it can never push the fly as fast as the car. This is because friction can only appose movement, so if the fly were moving toward the back windshield, friction can only slow down the movement towards the back windshield (that, and the air in the car is not moving faster than the car but I was hoping to not be that pedantic).
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