There has to be land records from North Carolina that may have a clue. These census records show that they owned the land they were living on.
Until I saw these census records I haven't seen Bethelem Bly called Hettie on any documents. I also don't understand why Bethelem was living away from her husband.
I'd also suggest checking for guardian papers for the Shook children. Prior to the 1860 census records the Parks were in Union County, GA. There is a paper trail somewhere that will explain the relationship.