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Aaron Pierson died in 1856 and Sarah Pugh Pierson was last seen in the 1860 Census, living with her son Lytle Pierson. So it is possible that she married McCool later.
The likely children of Aaron and Sarah were: Isham, Nancy, Margaret, William, Andrew Jackson, Lytle, Isabel, Emaline, and Ursula. (The first 4 are likely children, the others appeared in the 1850 Census.)
In the 1860 Census, there is a widow Nancy Pugh living next to William. Her children were Sophia, Calvin and Albert.