You are limited for time and trying to cram in far too much in your first post in my opinion but as Michael has explained, it's all about meeting your own goals. With the distances involved and having a little time to enjoy yourselves, I would think along the lines of; 25th and 26th] Explore SF. 27th] Drive to Yosemite and explore a little. 28th] Explore a little more of Yosemite and drive over Tioga pass [CA120]. Expect to take your time, you will be driving across the Sierra Nevada mountains and the stops/viewpoints are breath taking. Spend the night around Bishop on 395. 29th] Continue to Death Valley [Mount Whitney?] and into Death valley for the night. 30th] Vegas. 1st and 2nd Oct] Drive to South rim and meet friends or Sedona and then Grand canyon. 3rd] Phoenix and flight back.
Of course it is for you to do your own planning but you will be surprised how busy that will keep you, but at least give you some time to enjoy where you are going.