You have a fascinating rifle. It clearly shows the signs of being restocked by a relatively competent woodworker, so your family story about the restocking is probably accurate. The barrel seems a little short for this type rifle and may have been shortened when restocked, but the ramrod pipes appear well spaced, so all the work was done at one time.
If it currently is about .36 caliber, it's almost too small of a caliber to be an early flint rifle from KY. Without seeing the bore at the muzzle, I'd guess it has not been rebored, but rather had the original rifling grooves worn away, making the bore look smooth from years of use... suggesting the original caliber was even smaller. The presumed original bore size, and even current caliber, are almost too small to indicate an actual reboring.
Many current details suggest a Tennessee origin, or perhaps a Tennessee rifle used as the pattern when your family rifle was restocked. It's true that southeastern KY guns from the Cumberland Plateau region strongly resemble TN rifles as you get closer to the TN line, and this rifle could be from KY... but the restock gives the gun a strong TN appearance. The triggers, a little on the "clunky" side, hint at a TN origin more than a KY origin, as do the exceptionally thin butt and abrupt "break" where the comb drops to meet the wrist. The long 2-screw style tang could be either KY or TN. The current lock appears to be original percussion, and while it could have been changed when the gun was restocked, the smallish bore and lock combination suggest [to me at least] the rifle, even in its original form, was probably percussion.
It's always a great, and rather rare, occurrence today to have a rifle still accompanied by its original bag & horn... and even better when there is family history behind it. You have a family heirloom that most of us don't have, and at least a few of us are a little envious of.
Shelby Gallien