Whatever you do, don't take the route you described. That is the looong way around.
You say you're staying at Lake Tahoe? Which side of Tahoe? If it's safe to assume South Shore then what I would do if I was you is take 50 back to 395 and go south to Tioga Pass. I have done Tioga several times in my 35' motorhome with toad without problem, but it is a steep winding mountain pass with narrow lanes in some places inside the park. But motorhomes and tour busses do it all the time.
If you decide against that approach, then the best route is take 50 out of South Lake Tahoe and go down to 99. Take 99 south to 120 and then 120 east into the park. There is lots of roadwork going on on 99 and on I5 through Stockton, but really no easy way to avoid it.