You don't need to drive all that way north to see an old redwood park.
Armstrong Grove Redwoods National Preserve is near Guerneville and the Russian River, just 70 miles north of San Francisco.
You could have a nice day or two without all of the driving. If you go up Hwy 101 to Petaluma and then take the East Washington Blvd exit and drive through town you are on the Bodega Highway which goes to Bodega Bay where Alfred Hitchcock filmed parts of "The Birds". Continuing up the coast you pass several state beaches, then cross the Russian River. Turn right on Hw 116 and Guerneville is 12 miles away.
Then you could make a circle tour of it by following Hwy 116 to Sebastopol, then take Hwy 12, cross 101 at Santa Rosa and drive through the pretty Sonoma Valley, with lots of wineries. The historic town of Sonoma is built around an 11 acre Plaza from the Mexican days, which still has some of the original adobe buidings, now housing restaurants and boutiques and a couple of hotels.
You didn't mention an interest in wineries, but they are here if you wanted to stop. The valley is beautiful.
This would be a good place for an overnight...either somewhere in the valley or nearer town.
El Pueblo Motel, just north of town is a very attractive and reasonable property with gardens and a pool.
Or you could google to see if you could find cottages or a house in the Glen Ellen area. The Benziger winery does an interesting tram tour of its sustainable vineyards which the teens might enjoy.
Jack London State Park is here, with 800 acres of his "Beauty Ranch", his grave and house containing his papers. Lots of hiking trails. You can pick up picnic supplies at the market in town.
From Sonoma you are only 45 minutes from the Golden Gate Bridge, by continuing south on Hwy 12 to Hwy 121 to Hwy 37 to Hwy 101 north of San Rafael.