Melody - You appear to have run up against that "brick wall" we often encounter in records from early America. However, as you may already know there are four U. S. Censuses that list Robert Arms and by inference his wife and children. He is in the 1810, 1820, 1830 and 1840 census for Wilkes County, North Carolina. His wife, probably Martha, could be the 60 - 70 year old female in the 1840 census, so she probably didn't die on the "Trail of Tears."
Quite a bit of information can be learned from later census records for their children and their spouses. Also Robert's neighbors in the early census records list Fugetts(Fugates) and others who married his children.
As a Fugate who descended from the earliest Fugates who landed first in Maryland, I too have hit a wall at the parents of George Fugate and although I believe his parent were Martin Fugate, I have no proof and will not accept old family legends.For me, the best way to build a case has been to start at a point of proven facts and work backwards using only positively proved documents.
So you seem to have a lot of census records to start with and can build a good base.Good luck.