It's also important to be realistic about exactly how much you can do. Be generous with your timeline -- your travel times from A to B to C -- and you won't feel pressured to keep driving after the whole family's exhausted and crabby. Nobody remembers how tiring travel can be until about halfway through a trip, and by following conservative estimates and keeping your expectations down, you can make sure that every part of your family vacation is as leisurely and relaxing as you wanted it to be.
Likewise, remember that it's not a scavenger hunt. A family vacation means making memories together that you'll all remember forever, and that means taking your time and enjoying every part of the trip. You wouldn't waste a trip to the Louvre by rushing past every exhibit, just to check things off your list: The same goes for your family adventure. Flexibility is necessary, and if you need to skip one monument or state park in order to get somewhere more exciting for the family as a whole, make it a family discussion so nobody feels left out.
It's easy, in times of stress, to assert your control over the situation: A quick "I'm the one driving!" can calm things down in a hurry, if necessary. But remember why you're doing this in the first place. It may not be the adventure you planned, but it can still be the adventure you wanted.