I love the sound of this trip - we've done some of their others, always been excellent. Whilst I like the idea of being an independent traveller, we're not brave or outgoing and find that actually we have a better time, see more and learn more when we go in a group with a guide. But, I don't want to camp....unless anyone can tell me that US campsites are immaculate with fantastic facilities. It's not sleeping in a tent I don't like, it's the shared ablutions!
that tour is quite rushed and if you don't like shared bathrooms, it isn't for you. You'll also be helping with cooking, washing up etc etc.
There's nothing there you can't do independently. There are accommodations in all the parks of varying standards; for instance, the Grand Canyon has cabins in the village. But they get very booked out. Suggest a look in the Rough Guide(ask at your library) for suggestions. Flagstaff or Williams work for the Grand Canyon, Moab for Zion and so on.
there are towns within an hour or so of most of the parks so you can stay in a motel and not have to drive too far. All the parks operate ranger programs in high season for you and the kids so you can learn more that way.
We've toured round the area 3 times - it is very, very easy to do independently and the ranger stations at the parks have loads of information about each area so you don't need a tour guide. Use an itinerary of a tour you like the sound of and book it online.
I do all the driving as DP doesn't like edges. It is very straighforward, just get a US satnav. Get the "America the Beautiful" pass - ~$85 for all park access. I couldn't stand being in a tour group and looking around these amazing parks on a fixed schedule.
Regardless of whether you go with a group or not, try to go 'off peak' - I've been in September, February and April - all amazing; and all the more so when you get the parks almost to yourself!
And try to stay at The View in Monument Valley - a glass of wine watching the sunset over the rocks is just mindblowing. <fond memories> <weeps as no holidays booked this year>