"Caty" was b. abt 1759. Her parents were Rev. Philip Jacob Ehrhart and Maria Catharina Schremer. Philip's father was Philip Reinhard Ehrhart.
I think "Caty" was not actually there in the 1820 census, but the family owned the land. His son Philip moved to Davidson Co. TN and had children. His son Rev. Abraham Ehrhart married Catherine Forney and had NO CHILDREN.
So something is off. I do not think this is your connection.
There is a lot of Earharts, several different families, that lived in TN. I would search though those records in TN.