I wouldn't be quick to cut it out just because it was voted against since it sounds like it is important to you. Are there other plans over theweeks that nobody is too excited about? If everyone chose their top #1 thing to do, would Yosemite be yours?
Would it be easier to visit Sequoia National Park instead? I am not sure if that saves you any driving time or not. Yosemite is mind blowingly awesome, but I like Sequoia National Park better because it doesn't have as many visitors and seemed more natural. Yosemite is totally natural, but because of the number of visitors, they fence off all of the Giant Sequoias and there are lots of people everywhere. The parks have different feels to them.
Regarding Muir Woods by San Francisco, it's absolutely beautiful. The last time I was there, we didn't have a car so we took a "tour" that picked us up at our hotel in the city. We didn't have nearly enough time in the park. I did notice that there wouldn't have been anywhere to park if we did have a car, unless we got there very early, like park opening. We had to cell service there. If there was a way to take a taxi in and know for sure that they would pick us up at a certain time later, we would have preferred that. Just something to keep in mind. The trees are amazing, but there aren't any Giant Sequoias there.
I would want 2 full days inside the park. The 2 or 3 nights wouldn't matter as long as I was able to have 2 full days.
Are you doing all the driving yourself? Will you be taking turns? For years, I did the majority of driving for our trips and since I hate driving, finally decided that I wouldn't do car trips anymore. That got me some help. Now, I do about 50-60% of the driving, which I still hate. If you are doing all/most of the driving, you'll want a lot more time at each stop. People not driving get to chill out and space out and essentially have a break the whole time.