I'm almost certain this Hannah Coltrane was b. in Randolph Co., NC, dau. of William Coltrane & Elizabeth Elder. Her father d. in July 1822, and her uncle Richard Elder was appointed guardian of Hannah, and her two brothers David Coltrane & John Coltrane. The David Coltrane found in Forsyth Co., Cherokee Co. & Dawson Co. census records is her brother, with wife Winneford. John, the other brother returned to NC. Hannah's mother Elizabeth Elder Coltrane md. second William Smith, also of Randolph Co., NC and this family migrated to GA about 1826. William Smith & family are found first in Hall Co. Ga. 1830 census records, 1840 Lumpkin Co. census, as well as 1850,1860 & 1870. Does this profile fit your Hannah?