Grass doesn't grow in gravel. Grass grows in the dirt between the gravel. Get rid of the dirt and you'll get rid of the grass. You can throw any chemical you want at it, the grass will come back sooner or later.
Put new rock on the road and sooner or later dirt will get in the gravel.
There is an upside to growing grass in the drive. One, you are less likely to have pot holes. The grass will hold the rock in place.
Two, you are less likely to remove rock when you remove the snow in the winter.
I know a church that has about 3 inches of loose rock. No grass there, but kids will do donuts in parking lot throwing rocks all over the place. Can't keep the parking lot level.
So what's wrong with a little grass in your drive? Is it just the looks that bothers you?