Near Craters of the Moon (about 20 miles east of it) is the KOA in Arco. Probably more comfortable in summer, as it has hookups so you can run a/c. Stop by Craters for a bit, check out the visitor center, and then head on down the road to Arco. The Craters CG is unique & interesting, but no hookups and no showers. Just FYI.
BTW, Craters and Arco are on US 20, not on I-84/86. If you're sticking to the interstate and not traveling on a weekend, you might be able to find a site at Massacre Rocks State Park, about 10 miles west of American Falls, ID. Nice park, electric & water hookups. Your rig will fit in some, but not all, sites; we recommend the lower loop, as it will have less road noise. Some nice, family-friendly trails, not too long, and interesting history & view of the Snake River.
If you prefer to go not quite as far as Massacre Rocks, and are driving on I-84, a very nice private CG on the way is Village of Trees in Declo, just east of Burley. Not a lot for kids to do, but there's a path down to the river that campers can walk on, and there's a cafe onsite, open weekdays as well as weekends. If the kids will want to blow off steam, there's a KOA in Jerome, near Twin Falls, but we haven't been there, so can't comment on it.
2020 Toyota Tundra CrewMax 5.7L V8 w/ tow pkg, Equal-i-zer
2020 Lance 2375