From Palm Springs you could take CA 62 to Joshua Tree and see some of the Joshua Tree Nat. Park. Then make your way to US 395 north CA 247/18 would take you there via Victorville. Drive the Eastern Sierra. A Movie Museum in Lone Pine, the Eastern CA Museum in Indpendence, the Laws Railroad Musuem near Bishop.
Also, you could drive to the Mt. Whitney Portal from Lone Pine for a picnic there the climder begin their assent to Mt. Whitney.
The are a number of high Sierra lakes you can visit, many of which had lodging (Lake Sabrina, Convict Lake, June Lake) Mammoth Lakes Village is a 4-season resort with skiing in the winter, fishing, hiking, hoseback riding, golf, festivals and more inthe summer.
Stay north on 395 to Lee Vining and the Mono Lake Visitor's Center. Then backtack a bit to Highway 120 and go into Yosemite via Tioga Pass Road. After seeing the high country, Tuolumne Meadows, Tenaya Lake, etc. you can fight the crowds in Yosemite Valley. By the way, the Whoa Nellie Deli at the junction fo 120 and 395 is an excellent eatery.
When you leave Yosemite go out the north entrance via 120 to CA 49, the Golden Chain Highway, for a drive through the Gold Rush County to Placerville. Very interesting historic towns such as Jackson, Sutter Creek, Plymouth, Angels Camp (home of the Jumping Frog Jubliee), Sonora (the State Historic Park of Columbia make a interesting side trip near Sonora)and Placerville. At Placerville connect to US 50 into South Lake Tahoe. If the adults are interested there are a number of wineries in or near Sutter Creek, Plymouth and Placerville.
You don't say when you're leaving, but all of this route, outside the mountain area can get pretty warm in mid-summer.
You could also stay on 395 past Lee Vining going over more mountain passes, throught the Walker River Canyon and into Nevada, taking US 50 from Carsob City to Tahoe. If you go that route, consider a little detour to visit historic Virginia City, NV as well.
Have fun!

<<<You don't say when you're leaving, but all of this route, outside the mountain area can get pretty warm in mid-summer.>>>

The average daily high temperature in Palm Springs in July ranges from a low of 107 degrees to a high of 109 degrees. VERY warm

Thanks for all the great and detailed tips, boom_boom. We know it is going to be hothothot, but coming from freezing Norway, it can not get hot enough for us We need to "thaw'

It's okay, it's "dry heat" Seriously, if you're not in the direct sun, it's completely tolerable.

I like the suggestions above but would consider an overnight in Mammoth Lakes and a side trip to Bodie, a National Park that is an authentic ghost town in a fairly well-preserved condition.

If you stay in the town of Mammoth - it's pretty dense, so you might also consider staying overnight in June Lake - or along the June Lakes loop, right next to the lakes or river/streams.

http://junelakeloop.com/