Since you have been 3 times to Henry Coe, you might want to consider the Ohlone Trail. It runs 28 miles from Del Valle (Livermore) to Mission Peak (Fremont). It is a great hike right here in the Bay Area.
One idea would be to go to Point Reyes. Have a look at the map and pick something that fits the abilities of your kids. You could for example first go to the visitor center, look at the exhibits and hike the Earthquake trail (0.6 miles). My kids liked that at that age (for example seeing the fence that moved 20 feet in 1906). Then you can drive around to the youth hostel, park your car there and hike on the Fire Lane Trail to Cost Camp (1.6 miles). From there you can explore the beach, play in the sand and explore tide pools. The next day on your way back you can hike the Coast Trail (2 miles). On the map you will see other options (Glen Camp, Wildcat Camp). For a first outing they are most likely to steep.
Enjoy your trip,