So, how about.

day 6: drive from SF to Sequoia NP
day 7: drive from Sequoia NP to Yosemite NP
day 8: explore Yosemite
day 9: explore Yosemite
day 10: Drive to Stovepipe Wells DV.
day 11: Drive from S Wells to Williams AZ
day 12: Explore South rim
day 13: explore the South Rim
day 14: drive from GC to Vegas

On day 9 you could leave Yosemite just after lunch, sight see along Tioga pass and stop in Lee Vining to give you a little more time in DV and possibly make Furnace creek your overnight destination on day 10. Another option would be to revert back to skipping Sequoia and visiting Mariposa grove.