With more than 3 million visitors every year and most of them staying in and around Yosemite Valley, the valley can get pretty crowded especially in the summer. Private vehicles are allowed in the valley, but when you're driving and surrounded by such beauty, expect to be distracted. This is why I would not want to be the one driving. A long line of parked cars along the road could also put a damper on your full enjoyment of the view.
To fully take in the beautiful scenery and help ease the overcrowding problem, I suggest making full use of the free shuttle buses. They have regularly scheduled stops in various places of interest in the valley and they could even go some roads where private vehicles are off limits.
The shuttle buses are mostly free and could take you around the valley. There is also free service that go to the Mariposa Grove and up to Tuolomne Meadows. Some shuttle buses are tour buses or hikers buses that may charge a fee such as the one going up to Glacier Point.
The shuttle buses are convenient and good for the environment. And in this way, you don't have to worry about finding a parking spot each time you see a magnificent vista worthy of a picture.