One of the troubles with hiking the Great Wall with Small Children is that it is a very difficult hike. Maybe what Joel and I really need is a week or two of Grandparents visiting and watching the kids... then we can hike hard things without hauling heavy little bodies along for the ride heh heh.
Anyway, here are some links I've found for hiking larger or less popular chunks of the wall.
https://thecurioustravel.com/blog/best-place-to-hike-the-great-wall-of-china
This is a hike of three days or so--a bit short for my taste, but still good :P
https://www.chicagotribune.com/travel/ct-great-wall-of-china-without-tourists-20180316-story.html
This is a one afternoon hike. This Richard Fairbrother they speak of would be a cool guy to get in touch with..
https://www.reflectionsenroute.com/great-wall-china-planning-guide-checklist/
This is a list of various places to hike with different people's experiences at each one.
https://www.booking.com/searchresults.en-us.html?aid=941919;sid=bb980f49d66e79dd005034d2b9f2c5ad;closed_msg=6430788;dest_id=900054106;dest_type=city;hlrd=14&
Check out these cool places to stay around Mutianyu village! That might be a fun overnight with the kids for a more relaxed visit.
https://thecurioustravel.com/blog/best-place-to-hike-the-great-wall-of-china
This person says they went to the "Wild Great Wall, 120km north of Beijing", at Gubeikou.