Please help! Elizabeth (maiden name unknown) Patterson, b. about 1814 Hawkins Co., TN. Who were her parents?

She was my ggg grandmother, wife of George W. Patterson, son of Alexander and Betsy Patterson.

In 1850, she is a widow with sons Alexander S. (my gg grandfather), James, and George.

In 1870, she is living with Lucretia Smith, b. 1835 and David Smith (her son)? Her sons have moved to Stoddard Co., TN. One of those sons, George, is in the household of William and Rebecca Smith Messer in Stoddard Co.

In 1880, Elizabeth Patterson is in the household of Branch and Margaret Hicks Long.

She must connect to the Alexander Smith family, but how?

Any help would be greatly appreciated.