For children your ages I would recommend skipping Olympic, Ranier, Cascades, Crater Lake. The other destinations would be of better interest to the children.
Concentrate on Yellowstone, Grand Tetons and Glacier. It'll be more of a relaxing vacation for all of you and you won't be doing long daily drives. You'll be driving plenty within the parks themselves. Also, you won't have problems not having a towed vehicle. There are plenty of places to park within the parks.
Perhaps flying into Salt Lake City would be an option. You could perhaps work in Dinosaur Nat'l Monument in Utah then go up through Flaming Gorge and take 191 into Jackson, WY (excellent groceries just south of town on 89).
Grand Tetons - stay at Gros Ventre campground in the park to tour the southern half and do some things in Jackson (rodeo, chairlift at the ski area, trinket shops). Then move to Colter Bay RV (hookups) or Colter Bay campground (no hookups & next door), to do the top half of the Tetons. Plan on a gentle float trip down the Snake River in the park and you might see moose in the water with you. We did!
Then move into Yellowstone with a wide range of campgrounds. Fishing Bridge RV in the park is the only one with hookups and it's centrally located. Plan a new section of the park daily. It's huge.
Then head north to Glacier Nat'l Park. Take a 'Red Bus' tour if you can manage. Or stay at Apgar campground in the park and the free shuttle bus stops there to take you up Going to the Sun Road. You can get off and hike a little and get back on.
Perhaps leave the RV in Spokane and fly out of there. Sounds like a fun trip (and expensive)!
