This will let you view and record multiple cameras into the same video file, and it's free.
The problem you'll most likely run into is that webcams are pretty bad at capturing fast-moving object...like race cars. Also, webcams don't handle adverse lighting very well, such as low light levels, or looking directly into the sun. Since the resolution and frame rate are dependent upon the camera AND your system (which has to do all the processing), how powerful your system is will play a role in determining the quality of the video you can capture.
Here's a suggestion: buy a couple of inexpensive flip cams ($100-140). They take better videos, handle lighting and fast-moving objects better, and can be mounted and used both in and out of the car. It's not likely you're going to be editing video in the car anyway, so you'll have to move the video from the car to the desktop, so why not cut out the middle man? If it turns out you don't like what you're doing, throw them up on Ebay and recoup most of the expense.