We are planning on touring from Las Vegas to San Diego and up to San Francisco. The main reason for this trip is to go to Yellowstone National Park.
I hate to break this news to you but Yellowstone will be out of you way. Maybe you better check mapmaker.
Yup, you need to look at a map. Yellowstone is very far from California.
I'm pretty sure you mean Yosemite in California, not Yellowstone in Wyoming. Right?!
You didn't specify a point of origin so I can't give you detailed routing instructions. Neither did you mention where you will be staying. Do you have accommodations in Yosemite Valley? If not, where?
You didn't mention a time of year either. If you go during late spring through early autumn the whole park is accessible. If you go during late autumn through early spring, you'll have access to just Yosemite Valley. It's possible to spend just a few hours in Yosemite and that's better than never seeing it at all. But, if you enjoy Yosemite as much as I do then you'll want to spend as much time as possible there - two full days at least for a first time visit. There are numerous hiking trails, and don't forget about the giant sequoia trees.
Have a good trip. I know you'll enjoy Yosemite.
If it is in fact Yellowstone and not Yosemite then the best routing would be Las Vegas, Yellowstone NP ,San Francisco ,Monterey,San Simeon ,San Diego Las Vegas
Personally I find driving down the Pacific Coast Highway to be vastly superior in all aspects than driving up it.
A plan b and vastly more scenic [albeit slower ] routing from Las Vegas to Yellowstone would be to take the UT SR9 exit off of I-15 NB thru Zion NP and then find US 89 NB into Yellowstone NP