TurboJeep:
I'm not going to give you any specifics on "skip this and see that instead." As others have said, "to each his own." We did three cross-country trips of 32 days or more from 2004 to 2009, at 6300, 4200 and 8300 miles respectively with our kids when they were between 9/12 and 14/17 years of age (they are grown & out now, even though they're in my sig! :-) ) so I feel qualified to offer my perspective.
What I can tell you up front is for every one neat thing you want to see, you'll need to pass up 10 others. It's just a function of the vastness of our country and how much there is to see and do. I'll also tell you most of us easterners seriously underestimate how huge the western states are. That said, I love driving out there because you don't have the traffic congestion we do here (except for animal jams in the national parks.......) but they are big. VERY big.
As you can see from the mileage, the final trip was the most ambitious - 8300 miles in 35 days. Like you, we had some very specific goals in mind for the trip, and lengthening the time frame was not an option. We spent no more than 2 nights in any one CG; most of them were one night. Compared to the first two trips, the '09 voyage was more like a drive-by shooting. Don't misunderstand, I don't regret one moment of that trip and we saw LOTS of stuff. Our kids don't regret it, either. It was, however, a tight schedule and thankfully we had no emergencies or contingencies to throw off our schedule.
Your schedule is ambitious, but I think it's "do-able." Would I do it? No. Here's why.
For a moment, consider this question - what do you want your children to remember about this trip? Since we began serious trips around the country in 2001 we've visited hundreds of destinations & points of interest; national parks & monuments, state parks, amusement parks, historical sites, archeological sites and geological sites......you get the idea. But when we think back to those times there is almost ALWAYS an anecdote about something we or the kids did in a CG just hanging out. Or sometimes we'd discover something along the way that was really too cool to pass up and it turned out to be a phenomenal time. My point is this - allow your kids time to be kids. If that means taking a day to simply splash in a pool, play on the playground or just dig in the dirt, let them do it! Having a great time doesn't mean that every moment has to be structured and organized. Trust me on that.
Remember, the point of this trip should be to relieve stress, not induce it. Family time, as the credit card commercial says, is priceless.
Whatever you choose, enjoy & safe travels.