Using a car and motels will almost certainly be significantly less expensive than an RV, although it depends on whether you will want to have a separate motel room for the children. RV rental costs are high, fuel mileages are poor, and the overnight rates for staying in RV parks approach those of budget motels. However, many people feel that the very different lifestyle offered by an RV is worth the additional cost.

It would be a good idea to delay picking up the car or RV until you leave Boston. Any motor vehicle, especially an RV, is a liability in those cities, and there's a good passenger train service between them (Amtrak's Northeast Corridor).

I would suggest that you check your daily mileages on a map (Google Maps, etc). In some cases the places that you've listed are too far apart to be travelled between in one day. Therefore you'll need to cut down on your times in the cities a bit.

In the Yellowstone area, Grand Teton National Park (just south of Yellowstone) is also extremely excellent and well worth a visit. Personally, I would regard that as a much higher priority than Mount Rushmore but that's just my opinion.

Bear in mind that your husband will probably need to take an internal flight from Boise, Idaho before his long-haul flight.

BTW I'm just a normal forum member like you, not one of this site's official experts.