Whole lot of driving with little time to visit!!!!
1. LA to San Francisco----------7 -8 hrs driving
2. S.F. to Yosemite ------------4 hrs
3. Yosemite to Las Vegas-------8 hrs.
4. Las Vegas to Grand Cannyon--4 hrs.
5. Grand Cannyon to LA -------7 hrs
This is approx. and driving at 65 miles per hour with minimal stops for food or rest:( So 4 of your 9 days with be just driving. Leaving you with 5 days to discover and explore and relax. Personally, I would suggest you talk about eliminating 2 choices---Yosemite and Las Vegas:( Yosemite is beautiful but it is the high time for tourist and congestion). Las Vegas is a great time for adults and fun but unless you really enjoy eating out and gambling, there is not much to see. They do have some great night club shows. If you had 18 days for your trip then I would leave all the trips in.