I am one of the parents who could never figure out how to make the school system work for my child!
But, I have after schooled my child extensively and have come across some very useful resources.
These days, it is easier to provide the highest levels of enrichment, learning etc because of the internet. I suggest that you check out AOPS online classes, Alcumus, Udemy courses (they have multiple sales every year and are affordable), MOOC online courses, programming resources for Java and Python etc. You can cobble together enough resources to prevent your kids from being bored and also to experience being challenged academically.
You might have an easier time if you offered to run afterschool enrichment clubs in the rural school - you can offer to run Mathcounts teams, robotics clubs, lego clubs, chess clubs, math circles etc. There may even be other families that would be interested in pitching in for these type of activities.
Apart from these resources, there are many excellent video based courses from Coursera that are very convenient to watch and learn from. They are also reasonably priced if you shop around for them online.
Do your kids learn a musical instrument? You might even find a good teacher in a neighboring college town or city if you are living in an area with no one to teach music. Learning musical instruments challenge kids in ways that school academics do not. They also learn the associated music theory, improvisation, composition techniques etc that keep the brain engaged and challenged. And there is daily practice requirement as well that keeps them learning all the time.
Assign your kids appropriately challenging reading content in addition to what they are reading. Assigned reading is as important as reading for pleasure. If the rural area has no libraries, you could try to use a kindle or audible for downloading the books.
Good luck.
