My wife and I travel with our 6 and 4 year old sons in our dually and 11.5' TC. About the most distance I can do in one day is 350 to 400 miles. Any more than that and the kids are cranky and the wife is cranky. By the time you factor in all the bathroom breaks, food stops, fuel stops, and a little site seeing 5 hours or so was about all I had left for driving. I used to be a truck driver and do 10 to 12 hours a day but not now with the family. In my experience if you think you're going to drive 8 or 10 hours a day you will all be miserable.
What have you got against campgrounds other than maybe the cost? Campgrounds have playgrounds which are the best medicine for tired mean kids that have been cooped up all day in car seats. A swimming pool feels great after a long day on the road. It's a nice safe place to take a walk with the wife in the evening after supper. They often have mini-golf, ice cream stands, fishing ponds, etc. These are the things that really make me feel like I'm enjoying time with my family and seeing the country. Viewing everything at 70 mph thru the windshield just doesn't quite cut it for me.