How much time do you have for vacation? If it is 2 weeks you will be pushing it. You will average about 50 to 55 MPH and with 2 teenagers 12 hours each day on the road is pushing it. You won't have time to enjoy anything. We are planning a trip from the PNW to Disneyland and we are taking 5 to 6 days or more to travel to Disneyland. With a 5 day stay there. Average about 6 hours a day driving. Fortunately we have the whole summer to travel.
Your plan is to travel all the way accross the country and back, I'm assuming in 2 weeks, and enjoy Yellowstone.
Good Luck