2 nights in Yosemite is just about OK -especially if your accommodation is outside the park as there can be traffic queues in get into the park each morning. We were on a camping tour staying on a site in the park. Was a disappointing site, especially as we had been lead to believe all american campsite were amazing. tents all closely packed and the shower block was awful. The campsite was next to the Miners Inn in Mariposa. The Miners Inn looked fine.

SF - 3 nights is good; book for Alcatraz before you go and in good time - it get's booked up in the summer.

I’d say 3 nights in Yosemite, if you can. No, the campsites aren’t great but 3 nights only really gives you two full days for activities and there are plenty of sights to see and things to do, especially for families with older teens.
Just beware that camp spots are hard to book. Booking opens on 15th of the month, 4 months prior to you travel and you need to be on the phone as soon as the lines open.

Also for Yosemite, book your permit and do half dome when you do the camp booking. A pony trek will take you off the beaten track and have more chance of seeing wildlife etc

I’d definitely recommend more than 2 nights at Yosemite (we did 3 and would have happily stayed another couple - we just loved it there!)
3 nights in San Fran would be fine! If you want to do Alcatraz book in advance before you go we picked an early boat so wasn’t too busy when we arrived making it easy too see everything properly.

I'd agree with at least 3 nights in Yosemite - two nights only gives you one full day, which doesn't let you truly experience the feel of the place. I stayed in Curry Village some years ago and it was fine - very back-to-basics but let you feel like real wilderness. If you can at all, I'd say stay in the park.

I liked but didn't adore San Francisco. I think some of its special nature comes from the fact that it's quite a European-style city in scale and vibe, so that's wonderful if you're based elsewhere in the US but not such a dramatic change if you're from a similar place yourself. Two nights would be plenty for me there. I also found Alcatraz a complete disappointment - quite hammy and loads of focus on how tough the law enforcement was, not at all the sort of focus on compassion and reconciliation that I'd expect of a prison tour nowadays. There are far more interesting things to do in San Francisco.

Also, if you are driving, beware the almighty cost of parking in San Francisco. Depending on your schedule, it might be more cost effective to return your rental car on arrival there, and then commence a new rental when you depart San Francisco. Parking in the city is eye-watering.

Your trip does sound amazing! Enjoy.

We did 4 nights in San fran last year then drove to Yosemite. Stayed outside park in Mariposa. Did a full day in the park with Up close tours. They were brilliant. There were 3 of us and one other family in a mini bus the guide was fantastic and took us to places we would not have known to go to. Were picked up from our hotel about 7.30am so got to park before crowds. As we were there on 4th July it did get busy in afternoon but tour guide was able to alter route. Nothing was too much trouble and he was so knowledgeable and kept the 3 teemage boys on the tour engaged. This was the highlight of our holiday and wish we had more than 2 nights but also did the PCH after Yosemite. So much to see in a short time. I am definitely planning a return trip at some time in the future and would spend more time in Yosemite. Have fun..

We've done your trip in reverse, starting and ending in SF. We also stayed in Mariposa outside Yosemite at Yosemite Bug, which is quite 'hippyish' and our teen DD loved it. The camps in the park looked pretty grim tbh. Stayed for 2 nights.
On returning to SF we stayed 3 nights in a nice hotel, and also loved it. We did do Alcatraz and found it fascinating. We fought a bus to Haight-Astbury where flower power began. It's still quite an alternative place! As others have said, car parking in SF is extortionate and you absolutely don't need a car as public transport is excellent. pCH was nice, but we didn't see much because of the sea fog, which is around most days. Call into Big Sur and Monterey. We also stayed in St Louis Opisbo and DD had surf lessons off a Californian surfer!