In my opinion, using an RV for such a trip would be a good option for you, when you take such a long trip. A 24-foot motorhome is just large enough for your family, it will have room for everyone, and you can still stop at a motel when you need a shower or whatever.
The one thing I do recommend is that whoever you rent from that you make them give you good instructions of how to dump the holding tanks. You see, they hold the waste water and sewage from the sinks, and showers and the toilet. Dumping them is a simple process and they usually hold the waste from up to a week of NORMAL use. I assume you will be staying at a campground when you get to CA, so typically your campsite will have a dump connection. If you're going to park at someone's house then ask them to find you a place that has a dump station you can use when necessary.
You can plan your trip to stop and even stay overnight at places such as; Rest Areas (that have nighttime security), truck stops (a little noisy), Walmart parking lots (ask management for permission), etcetera. Or pick a campground chain such as KOA and call them to set you up with the right KOA campgrounds where you have overnight freedom to use their pool, restrooms, electricity and water hookup, and the run of their amenities.
I know I'm putting a lot of emphasis on these things, but if you plan ahead you can have a great trip, stop where and when you want, fix your own meals, and have a relaxed trip.
I envy your, traveling through such a great and beautiful part of the USA.