Can you get a leave of absence at your job? Many places might be willing to work something out for what is basically a once in a lifetime trip. They may also be willing to let you carry over some time from year to year for a special occasion even if it's not standard policy. It never hurts to inquire. (They may also be rigid and inflexible....)
Two weeks is not enough to drive to the west and do anything and drive back, IMHO. I can drive in a car from Vermont to San Diego over the course of five days, but those are long days and without stopping to see anything on the way and, of course, in a car that makes better time than an RV. Even in that case, two weeks (plus a "free" weekend) would mean a grand total of six days in California.
If the school is willing to send along work, possibly you could arrange to have five or six weeks around New Year's by combining vacation from two years and getting four or five or six weeks at a spell. That does rather limit the practicality of seeing some areas in the north, such as Yellowstone.
Your 13 year old might surprise you with the desire to travel as time goes on, too. I was once 13 years old (a fair few years ago), but I'm planning on taking a long cross-country RV trip with my mother this summer. I would have jumped at the opportunity at pretty much any age.