You only need one camera to achieve what you want. There was an old (~ 10 - yrs) DARPA(?) project which used an artificial neural network to control the steering as you described. My MSc dissertation (a game playing virtual "tank") was influenced by it.
The basics were as you described, take the video feed, then whizz up the contrast to black and white. You then end up with the white lines as two edges of a "trapezoid". The neural network was trained so that the car was kept in the centre of the trapezoid (this is the hard part).
There is a link here
http://society.kisti.re.kr/~Eksae/_notes/data/pdf/v3n2_5.pdf[
^]
to a similar project.
This will be an interesting project!