I would add as many days as possible, the west is huge is your covering a lot of ground. Driving can be slow, especially in Yosemite and along the coast, just prepare yourself for it.
Figure about 2 days in Yosemite, depending on where you stay. The very underrated top, along Hwy.120 from Tioga to the Valley is incredible. Lots of cool short hikes and excellent view points that dad would love.
Then a full day in the Valley, yeah it's crowded but absolutely jaw dropping. For the Valley start early, like sunrise or even earlier and beat the mob, lots to do-see.
Do your best to stay in the Valley, again keep trying a few times a week for reservations, at least.
There are a bunch of cool hikes in Yosemite, the park provides very good information and maps, see what fits you and Dads needs. https://www.nps.gov/yose/planyourvisit/hiking.htm
If you can add a couple nights, maybe add 1 for Humboldt, try and stay in "The Avenue of Giants", really beautiful area and maybe one to Seattle.
You might enjoy " Trees of Mystery " just north of Klamath, very tacky advertisement along the way but a nice museum, folks here like it.
Also keep an eye out for the Elk Heard by Orick.
FYI, the National Redwood Parks are very average at best, the 2 best Redwood Groves are in Humboldt and Jedediah, IMO.
Lots of cool small towns, good variety of eats, micro brews-wineries and of course killer scenery along your route!
Get a cooler/ice chest before you leave LA for drinks and ice, you'll need/want it.
Oh yea, if you do head to Mammoth Lakes from LA. If it's on a weekend leave by around 9-10am, if not earlier. If it's on a weekday be on the interstate by 6am and beat the traffic, very important for a decent semi relaxing drive. By 6:30-7am the traffic will be getting very heavy, bumper to bumper.
Actually the same for heading up the coast. LA is a mess, traffic wise.
Forgot, Mammoth has lots of good hikes and Mtn. biking.
Maybe take the tram up to the top of the mountain for great views and ride a bike down. Dad can ride the tram back down.