Hello and welcome to the R.T.A forums.

I would recommend travelling to the south rim and taking it all in, the sunset/ rises are amazing and it will give you time to go to some of the many viewpoints. I would allow 41/2 to 5 hours for the trip from Vegas, plus a little extra if you want to stop at the hoover dam for a while or take a side trip onto an old part of route '66, but you may want to get an early start and go direct to the canyon as you won't have much time to spare the following day.
The drive to L/A is a long one and you will probably want to get going fairly early again.
I would allow 10 hours for this journey, so it will a full day.Have you another day you could squeeze from your trip for this part?

If we can help you with anything else ask away :-)