Alexismom, this single mom and her 16 year old son (named Alex, btw!) did this road trip last summer! I have to say that if your ONLY aim is to take your daughters to Mt. Rushmore, then save your money for airfare instead. It is a long haul to Mt. Rushmore, especially since you'll be the only one driving. I totally agree with making a full trip of it, to include Yellowstone at the VERY least. Your daughters will not forget the geysers and the other sites there. Here's a rundown of our trip and stops last year:
Day 1: Departed Puyallup at noon and stayed overnight in Spokane (5 hr drive)
Day 2: Departed Spokane around 8 AM and arrived in Bozeman (6 hr drive)
Day 3: Departed Bozeman, arrived at Yellowstone in approx. 90 minutes. Spent this day and the next 2 days in Yellowstone (tent camping).
Day 4 in Yellowstone. Lots of sites and driving.
Day 5 in Yellowstone; took a drive BY Grand Tetons down to Jackson and back to Yellowstone (about 5 hrs of driving) BEAUTIFUL view of the Tetons (and my Prius managed to get a whopping 62 miles per gallon that day, for some odd reason!)
Day 6: Departed Yellowstone 7 AM. Hard drive all day to Rapid City , SD (8 hour drive). Beautiful drive through Big Horn Nat'l Forest, but some white knuckle driving for part of it. You might want to get back up to I-90 instead of driving all the way through Wyoming.
Day 7: Mt. Rushmore (for all of a 2-3 hour visit! Bonus: Kate plus 8 was filming there. I think they were there for all of an hour, most of it being spent in the gift shop while the little ones huddled in the cold fog outside with their nanny), Custer State Park (should have gone there first thing in the AM, when more of the animals would have been out) . The drive all the way around Custer took about 3 hours, with a few stops here and there.
Day 8: Continued east for a daytrip to the Badlands. My son loved climbing on the rock hills. We also toured the minuteman missle site (one of my favorite stops), and made a pit stop at Wall Drug (tourist trap that it is...it's huge, and there are entirely too many people there at any given time.) Stayed over in our hotel in Rapid City.
Day 9: Left at 8 AM, heading home. Made a little detour to see Devil's Tower Nat'l Monument. Continued driving to Bozeman, MT (8 hrs)
Day 10: Bozeman to Spokane: 6 1/2 hrs
Day 11: Spokane to home (5 hrs)
For any road trip, I recommend buying a travel atlas so you can see where main cities are. Then use Mapquest or Googlemaps to see the distance and driving time estimates between cities you may stay overnight in. One thing that you can't see on Mapquest or Googlemaps is the terrain or elevation. A good atlas will show significant elevations (and mntn passes), as well as mountain ranges. Our drive conditions in the Big Horn Nat'l Park were a complete surprise to me because I failed to look at the map closely when planning. It was a beautiful drive, one of my favorites, however.
Camping will definitely keep your costs down, but you should pre-book your nights ahead of time when you are visiting popular areas.
I am currently wrapping up planning for this summer's trip to Utah's National Parks. I didn't want to spend 4 days driving there and back, so we're flying in on this one. We still have a tight squeeze for our 12 day trip!
Please feel free to message me with questions, if you'd like!