long-hours not the only thing
Driving the Interstates as a professional is not the same as driving the hours necessary to see that much country in three weeks. Remember, in the national parks the best possible speed you can do is an average of 30-35 mph. If you factor in the stops to check out the waterfalls, the animals, the people... driving speed in the parks will be closer to an average per day of about 10 mph.
While you may be capable of driving 12+ hours per day is your family equally able? Plus there is so much to see in between the parks.
On the other hand, a conversion van is just about perfect for being able to travel the parks in comfort and style. My only caveat -- might be to cherry pick 2-3 national parks and really enjoy the experience and trhe road trip. I personallly have made the trans-USA run numerous of times in the 3 day stretches -- but I was never pretending to be on holiday. You are going there to have FUN -- not set personal records for driving endurance!
Slow down, enjoy the journey. Check out Megan's thoughts on the "Art of the RoadTrip" at http://www.roadtripamerica.com/mftdb/053198ca.htm
Mark