I live in Calaveras County - may I suggest you stay the night in Murphys? It's on your way to Angels Camp from Big Trees. It's a super cool funky artsy town with lots of wineries and great eateries, I highly suggest Alchemy. Then you can take Parrots Ferry road to Columbia, which is totally worth checking out. Angels Camp and Sonora are nothing much to look at, but Murphys sure is!
Bear in mind that it will take you around 2 1/2 hours to drive from the Sacramento Airport to Arnold (where Big Trees is) depending on the day of the week. It's worth taking CA 49 rather than 99, you'll see so much of Gold Country. It would probably be best to do only Big Trees on your arrival day as by the time you get there after getting your car, luggage, and lunch it will be coming on 2 and you'll want several hours there at a minimum. There is a $10 parking fee cash only to keep in mind.
Columbia is awesome with gold panning and such but would most likely take you less time so it would be easier to do it the morning of the day you leave for Yosemite. It's around 2 1/2 hours to get from Columbia to the Yosemite Lodge. I hope this helps and I'm always happy to answer any questions about my little part of the world!