If she was a Butler, she would have had to have been born before 1695, as John Butler who married Anne Baynham was most likely the fellow who left a will in 1677 in Westmoreland County, Virginia. For inference, Sarah Butler, daughter of John Butler and Anne Baynham, was born in 1674 and was married to Benjamin Berryman and had a daughter, Elizabeth, by 1699 -- four years after you say Mary Butler was born to John Butler. Perhaps there is a missed generation somewhere...though I agree in conclusion that the Butlers, Baynhams, Peytons, Wrights, and Coxes of Westmoreland were indeed related to the Washington family.