A Few Basics to Keep in Mind
While it's true that driving between Maine to California (e.g.: Portland to San Francisco or Los Angeles) can be done in six days, that really only accounts for the driving and a very few short time-out sort of stops each day. If you plan educational stops, and maintaining a pace that doesn't wear out your kids, you'll probably need closer to eight days each way, leaving only five to seven days actually in California. On the plus side, on long cross-country trips such as the one you're planning it is very easy to take two completely different routes, one west-bound and another eastbound, so that you're constantly driving through new areas and passing new historic, scenic, and just plain interesting sites. Finally, as well as historic and scenic sites, there are historic and scenic roads. Among them are the National Road that opened up much of the nation to westward migration, the Wilderness Road through Kentucky trailblazed by Daniel Boone, the Natchez Trace which allowed boatman to return to the Midwest after floating down river in the days before steam power, I-80 which follows the old Oregon Trail along the Platte River in western Nebraska, and the Santa Fe Trail among others. And don't forget the role played by rivers, most notably the Ohio and Missouri.
Then there are a few logistic items to make sure that you take advantage of. The first is to get an America the Beautiful annual pass that's good for admission to all national parks, monuments, and historic sites. Since its 'year' begins at the point of purchase, you should simply buy one at the first park you come to that charges an entry fee. The other resource is even better since it's free, and educational. That's the Junior Ranger Program which will give your children some age-appropriate activities to help them get the most out of their visit to each park, and upon completion rewards them with some very nice souvenirs including, typically, certificates and badges.
Those are just some things to keep in mind as you set up your first proposed itinerary. The other major consideration is what your children want. Be sure to include them in the planning - They'll surprise you, I'm sure. And once you have your own ideas of how you want the trip to go, be sure to check back in and see if we can offer some specific sites on or near your route(s).
AZBuck