It would appear to me by your explanations that you have a solid body alignment, working tempo, and grip setup for your irons and hybrids. I'll call that your ROUTINE. In contrast, your ROUTINE for driving is all over the place, hence the wide variety of hooks and pushes. To help you quickly improve in driving, I recommend the FART system. Perform it in order and it's easy to remember haha. I came up with FART for my 9 year old son (right-handed golfer)
F - Face, Get the club face pointed where you want the ball to finish
A - Alignment, Align your body in the direction of your swing. Where your hips point, your knees, feet, and shoulders should also point.
R - Right hand, will you take a strong grip or neutral grip? While R is for right hand, also pay attention to your left hand. How many knuckles do you see on your left hand? The more knuckles you see the more AGGRESSIVE the grip is, and will likely cause you to draw and hook the ball.
T - Tempo, You need to establish a consistent tempo and sequence. Think Power and Grace. For me, if I try to speed up early in the transition from the backswing to the downswing, I tend to impact the ball at a point when my hips have not opened up yet, which causes me to hook the ball.
Of the four letters, I think R has the highest correlation to helping you fulfill your intended shot; because you have to turn your hands over naturally, and how you set them up to begin with will determine how much or how less you can turn them over.
Hope this helps you!