The Divide in Montana, Idaho, and Wyoming
Good move to get your sons out into the mountains. Mine are the same age difference (though now 33 and 29), and we took them to Montana for 2 weeks of off-highway exploring in 2000 when they were 16 and 12. They loved it.
Anyway, a search using "ADV + Continental Divide Trail" and perusal of the Thumper Talk forum, ADVRider forum, AdventureBikeRider.com, and many road cycling (bicycling) forums should produce many hours of material in the form of maps, blog posts, pictures, etc. An outfit by the name of RawHyde Adventures does a truck-supported dual-sport Divide Ride every summer and their website is a good resource.
Aside from digital mapping tracks, of which I have none, I'd be purchasing a Benchmark Road and Recreation Atlas for NM, CO, WY, and MT. There is enough overlap from MT and WY to cover the ID adequately. Your investment in the 4 Benchmarks will run you $100 or so, but IMHO there is no better tool for trip planning and even close-in navigation. Of course you'll have a GPS and perhaps some USGS quadrangle sheets downloaded onto a tablet such that you can pull them up without a cell signal (which you won't have in much of Montana and Wyoming, at least), but the Benchmarks are the gold standard as far as I'm concerned.
It's also very helpful to look up "Backcountry Byway" maps. The Federal Gummint promotes off-highway tourism in areas all over the country by distribution of downloadable brochures featuring "backcountry byway" maps. In Montana and Wyoming, they're mostly guides for graded gravel road travel within large swaths of National Forest and Bureau of Land Management (NF and BLM) lands. Of particular interest to Divide explorers would be the Lewis & Clark Backcountry Byway in MT and ID and the Big Sheep Creek Backcountry Byway in far southwest MT. The former includes Lemhi Pass, where L&C first crossed the Divide (and which should be a focal point of any Divide exploration) and the latter includes around 60 miles of very remote cattle and sheep ranch country running parallel to the Divide on the MT side and is along the recommended Divide cycling and moto routes.
Not within the Backcountry Byway system, but a much-discussed part of the Divide Trail, is the Centennial Valley in Montana. It runs E-W, on the east side of I-15 immediately north of the ID border, for about 60 miles (all gravel) from Monida, MT to Henry's Lake, ID, crossing the Divide at Red Rock Pass. Near Red Rock Pass is Brower's Spring, the true source spring of the Missouri River, located at the headwaters of Hellroaring Creek on the MT side.
With the boys in mind, first-rate recommendations for a July visit to Montana would include a half-day in Butte to see the Berkeley Pit as well as the great mining museum there. Annually on the 3rd weekend in July is Bannack Days, at the authentically restored ghost town of Bannack, MT. Bannack was the first capital of Montana Territory for about 18 months and Bannack Days features cavalry reenactors, frontier land survey reenactors, Dutch oven cooking contests, and some of the finest pies on the planet available for purchase. Bannack is close to the Divide just outside of the Big Hole, and you'll definitely want to cruise the Big Hole from Wise River through Wisdom and Jackson to Bannack. Near Wisdom is the Big Hole National Battlefield, an entirely sobering NP facility located along the Chief Joseph Trail. The Battlefield made a big impression on my boys in 2000. I'd also search up the location of the 2017 "Chief Joseph Ride". The CJR is an annual event in which participants, many of them Native Americans, spend a week riding and camping along a segment of the Chief Joseph Trail in various parts of ID, MT, and WY. The participants ride genuine Appaloosa mounts and have a moving camp nightly. A visit to the staging area on the day prior to the start of the ride would be very cool. We did so in the Big Hole in 2010 and my wife, once a big show horse gal, loved it.
For a break in the action, and to get the dust off of both you and the boys, book a mid-week night or two at Elk Lake Lodge at the head of the Centennial Valley in Montana. ELL is an off-grid complex of a few very nice cabins and a combination lodge, restaurant, and bar right on a 150 acre lake. Generators and solar provide juice for the cabins and the very, very good restaurant.
Get your guys involved in the planning and they'll enjoy the trip even more.
Foy