Driving sim games really won't help you in my opinion. Being in a real car, with real vision and pillars blocking your vision cannot be accurately simulated, as you're not going to be doing any moving your head, shoulders, feet, eyes at all in the way you would be. Ask your instructor to give you more time on them or, practice in another car if you could get access to it.
But, if you're just going for the fun of it, Try Live for Speed, that's free and the driver training things / free drive tracks will probably give you an idea on the dynamics.