Got any racing simulation games (gran turismo, forza) ?
If so, play these for about half an hour, then go back to vice city. Your car control goes up by like 200% If not, time for learning how to drive in GTA.
The key is acceleration. Never stop accelerating. When you need to corner, get out wide, and perform big, sweeping turns, to minimize braking. If you're getting understeer (where your car doesn't turn enough) , keep the throttle down, and tap the handbrake to force the car to drift into oversteer, keep tapping the more you need your car to turn.
If all that fails, I'll install VC later and give it a shot.