Maybe this can help. Possibly William could be somehow related to your Elizabeth and possibly the Elizabeth name was passed to Mary Elizabeth. Pure speculation though. I only know that William and Amelia are from PA not where in PA.
I have the following information on Duck. This is unconfirmed.
William Duck (PA) and Rouah? (order unconfirmed) 1. Amelia Duck (b. June 29, 1840 d. April 25, 1917) m. Charles A. McFall 2. Fredrick Duck 3. William Duck 4. Daniel Duck 5. Simon Duck 6. Mary Elizabeth Duck 7. Sarah Duck