A very sad day indeed, but what a blessing your Sportscoach sacrificed itself to save your lives. So sorry to hear about the other driver. It sounds like you both have the best attitude you could possibly have, considering the circumstances. Best of luck to you, and to the grieving widower as well.
I would also recommend a popup. We (2 adults, no kids) LOVED ours; kept it for almost 17 years. For a young family, keeping things simple, storing in a garage, and towing with a smaller SUV, it would be perfect. Newer ones will tend to be fairly large, but I'm sure you can find some smaller models that will fit your needs just fine. Welcome to the RVing life!
Make Yellowstone & Tetons reservations NOW. The parks are less crowded than in midsummer, but they are by no means emptied out. In addition, some of the CGs inside the park close after Labor Day. (Outside the park most are likely to remain open at least through most of September). Glacier's season usually ends fairly early, so be sure to check on season closing dates there as well (and I'd recommend reservations there too.) Good CGs for Yellowstone: the only CG inside the park with any hookups is Fishing Bridge, which is centrally located, but sites tend to be tight. (On the other hand, you'll probably spend all day & into the evening driving around the park to see the sights.) Outside the park, we like Grizzly RV Park in West Yellowstone; it's close to the west gate of the park, very nice, clean & plenty of room for all sizes of rigs.
Since we need hookups, we have chosen Colter Bay RV Park for the Tetons. For your size camper, if you can deal w/o hookups, you might consider Colter Bay or Gros Ventre CGs (not to be confused with the RV park) - Signal Mt CG will be too small for your camper, however. (Sites too short.) IMO there aren't any other private CGs that pass muster in GTNP and Jackson - of course, that's our personal taste.
If you can, be sure to allow at least 3 full days for Yellowstone and 1 full day for the Tetons. If you are active & enjoy hiking & other outdoor activity, add a day (minimum) to each park. For Glacier, I'd recommend allowing at least 2 full days, and 4 would be better. If you can, divide your time (and your campground bases) between west & east side of Glacier; they are very different from each other. Remember you cannot pull your trailer over Going to the Sun Road; you'll have to go around, on US2. It's a nice drive too, but doesn't compare. The red bus tours, if still operating when you are there, are wonderful, worth every penny, IMO.
Have a fun trip!
We looked at the West Glacier KOA but aren't a fan of camping without trees. Agreed. The West Glacier KOA is a very nice CG, and tours of Glacier NP pick you up right at the CG (they don't do that for any of the other CGs outside the park, that I know of). But when we had made our reservations for it, we were looking at old pictures and were looking forward to camping in a pine woods. Got there - almost no trees! Turned out they had cut many of them down to make room for bigger rigs and those who want satellite connections. :( We enjoyed our stay, but would sure have loved the woods. I believe it was Mountain Meadows we drove into & peeked at, and they are quite wooded.
There are several parks in north western Illinois that butt up against the Mississippi River. Thanks for the reminder! Thomson Causeway, a COE CG on the MIssissippi is a nice spot. A few campsites are right on the river; others easily walkable, only yards away from the river. Not exactly your peaceful little creek, though! :)
Nice scenery along that route, at least once you're past Bozeman. (You may be driving thru parts of town there.) Sorry, I don't know about construction; there's usually some somewhere in this area during the summer, since there's such a short season for it. Grizzly is a great CG choice, IMO.
While along I-90, I hope you have time to stop at the Little Bighorn National Battlefield for a day (2 decent CGs nearby for an overnight). It's well worth the stop. And of course Devils Tower is off I-90 and worth a stop as well. The KOA there is right at the base & has great views of the tower; there's also a no-hookups NPS CG inside the park.
Have a wonderful time in Yellowstone!
Henrys Lake SP in Island Park, Idaho (next to a lake where fishing is allowed); Riverside (NFS) CG in Palisades, Idaho; Toad Suck CG in Arkansas (COE?); several NFS CGs near Stanley, Idaho (along the Salmon River) and at Redfish and Stanley Lakes (same general area), on lakes with fishing.
x2 on the Rustic Barn. Nice place, out in the country, electric & water hookups and a honey wagon, decent showers, etc.
There are also some great state parks in sw Wisconsin, including our personal favorite (Wyalusing). They don't have water hookups, though (just electric) and even then, not in all sites; reservations are taken 11 months in advance, so you might have trouble getting in on a weekend without planning far ahead.
As most have said, don't bother with alternates. 80 isn't that bad (nowhere near as bad as 90 and 94, which go through the city itself). Try to avoid rush hour (6-10 AM, 3-7 PM) if you can; rush hour will be just as bad on all the non-interstates as well.
Mountain Directory West would be helpful to you as well, showing grades and passes that might be of special interest to RVers and truckers. You should be able to find one at truck stops or some of the larger/better-equipped RV supply stores. The routes along the river might be slower, but potentially prettier. :)
Some communities forbid the use of jake brakes. (Usually there are signs to this effect.)
One comment on putting dad/sister in the dinette or couch - this won't work well unless they are very short. In our experience, these extra "beds" just aren't made for anyone larger than pre-teen children (and even some of them may be too tall for them) A bunkhouse TT might work well in that case. The bunk areas can be used for storage when it's just the OP & companion.
While at Arches, consider staying an extra day in order to include Canyonlands NP. Moab UT has several campgrounds; we stayed at Spanish Trail, because it has a little shade (many don't in that area). Dead Horse Point SP is near Canyonlands & is a great place to stay; electric hookups available but you will need to bring your own fresh water.
Ditto on Grizzly RV for Yellowstone. If you can do without hookups, there are several CGs inside the park, but I would strongly advise reservations. Colter Bay RV Park, IMO, is by far the best place to camp for the Tetons if you need hookups; there are several good NPS and NFS CGs in the area there. Other private CG offerings there are not to our liking.
Lots of good CGs in the Black Hills (for Mt. Rushmore.) While there, make sure to visit Crazy Horse Memorial as well. Our favorite CG there was Rafter J Bar Ranch Campground in Hill City.
Don't miss Devils Tower on the way from there to the Yellowstone area; the KOA right at its base has an amazing view!
Depending on the size of your rig and if you need hookups, there is a CG right in Crater Lake NP. Haven't stayed outside of the park there. (We camped there in a popup, so no problem finding space in a campsite. However, we did have reservations.)
I hope you have allotted a lot of time for this trip. One day per park just won't cut it, especially for Yellowstone, Zion and Arches/Canyonlands, and the Black Hills. And I do recommend advance reservations, depending on the time of year & size & needs of your rig.