On occasion, I have a problem with too much right hand (I'm a righty) turning the club over. Here are a couple exercises I use:
1. Setup to the ball and take your normal grip, now take your trailing hand and while leaving it on the club, point your pointing finger and thumb like your shooting a gun. Swing the club like this, making sure that your thumb and pointing finger stay off the club. This was an exercise I saw on the Golf Fix on the Golf Channel. It's a good exercise to prevent that rolling over feeling and will work well with the driver.
2. Hit balls with your leading side. If you're a righty, hit some balls with your left arm. This is more suitable for irons and hitting off mats but I really like the feel it gives for timing and squaring the club at impact.
3. Practice using a double overlap grip. It's the same as a normal overlap but instead of one finger, you overlap the pinky and ring finger. A while back I was having problems with some snappy pull hook problems and my teacher gave me this and #2 to work on. I practiced using the double overlap and liked it so much that it's my normal grip now.
Hope these help. Have fun.