From Jackson you are only an easy drive to Yellowstone. Tetons are beautiful, a raft trip on the Snake is a hoot the kids will remember for life, but Yellowstone is among the best of the best. If I could only take my kids to one NP in the country it would be Yellowstone. As for Redwooods NP, I loved it. There is a very nice campground right on the Klamath River just north of the park where we stayed. The mouth of the river meets the pacific right there. The hike from the visitor center to Gold Beach goes right thru the heart of the giant trees, shady all the way but a fairly long hike if kids are small. I pulled a big 5th wheeler on 229 to Redding. The scenery is great and my truck had a 4.10 rear too so you should not have a problem. You will hit bigger grades elsewhere in your trip. I liked both the Custer Battlefield and Devils Tower, nice KOA right there (have the kids seen the movie ET?) better than Mt Rushmore which is a total tourist trap. And The Badlands are well worth a visit. But you really should see Yellowstone. In two days you can see the main attractions, Old Faithfull, Yellowstone Falls and canyon, Hot Springs, etc. They all have easy access from parking areas. I have done back country hiking in the park, but most people never leave the park loop road, and with small kids you really shouldn't. The next time out there try to make it to Glacier NP. That's my alltime fav. When the kids are all a little older the hiking trails on the east side (St Mary's, Many Glacier) and the "Going to the Sun Road" are breath taking.
