Thank you for the additional information.
Have you been able to rule out the following family? (I have to get back to gardening, so I can't take the time at the moment to do so.) Could Minnie be a nickname; her age isn't quite correct, but it's "close". Also, the father's name (and age) doesn't match with your possible name of John Davis.
1880 Pittsburgh Census
Joseph Davis, age 44, born England and his wife Mary G, age 43, born England and their children
Benjamin, age 22, born England
Elizabeth age 17, born England
Joseph, age 14, born England
Sophia, age 12, born England
Thomas?, age 11, born England
Arthur ?, age 6 [name lined out?], born PA
? A, age 5/12 [name lined out?], born PA
Minnie, age 23, daughter-in-law, born PA, parents born Bavaria
Joseph, age 3, grandson, born PA
Address: Arlington Avenue