This house has now been identified!  It is at 916 Oakmont Avenue (previously known as East Railroad Ave) in Oakmont, PA, and was the home of John Porter Hunter and his wife Mary Hannah Agnew Hunter.  They sold it to the Baileys in 1902.  It is shown as lots 4,5,6, and 7 of the J.W. Dalzell plan in the 1886 - Atlas of the Vicinity of the Cities Pittsburgh and Allegheny: Plate 11  at http://images.library.pitt.edu/cgi-bin/maps/showmap.pl?client=maps&image=86v01p11.  See also a Hulton subdivision plan from 1884.  It is also shown as the Bailey property in the 1903 Eastern Vicinity of Pittsburgh map at http://images.library.pitt.edu/cgi-bin/maps/showmap.pl?client=maps&image=03vevp32.

The Allegheny County assessment photo of the 916 Oakmont Ave house:  

The white house in this photo from my grandmother was the Elizabeth Bradley Home for Children at 214 Hulton Road (earlier designation H Street) in Oakmont, torn down in the '70s for the new Riverview High School.  It was apparently originally John Agnew's home.  He died in 1905, the year the Bradley Home was established. However, the house was purchased by the Bradley Home from the Dalzell family.

This house is pictured in Oakmont (Images of America) by Vince Gagetta, Paul A. Calabrese, Cheryl Zentgraf, Gary Rogers, Arcadia Publishing (SC) October, 2003, and identified as the home of the owner of the Agnew Glass Company:

The photo below was given to me at the Oakmont Library. I was told that it shows the former Agnew home when it was the paint laboratory for the Thompson Paint Co. in the 1940s. The original house is on the left, with a later addition built by Thompson.  (source: Oakmont Carnegie Library)

Addresses I have for our family in Pittsburgh include:

Year	Name	Address
1855-1880	John Agnew	Carrick, Baldwin Township, 1915 Brownsville Road, intersection of Brownsville Road and Agnew Road.  A 1916 map shows the Agnew Apartments at this site, possibly in the old house. This house is no longer standing.  today the neighborhood is a modest one of mixed commercial and residential development in Pittsburgh's South Side.  Houses in the neighborhood date from the 1920s. Currently a state assemblyman has his local offices at 1917 Brownsville Road, which appears to be the oldest building on the Agnew site.
1895	John Agnew	Hulton Station, Oakmont factory at 159 First Avenue, Oakmont; residence in Oakmont
1895	John Porter Hunter	Hulton Station, Oakmont
??-1902	John Porter Hunter	916 Oakmont Avenue, Oakmont previously known as East Railroad Ave.
1905	John Porter Hunter	1019 North Highland Avenue, Pittsburgh current photo from Allegheny County Assessment site house built in 1884; 4 bedrooms; current market value $241,500
1912	John Porter Hunter	5819 Wellesley Ave., Pittsburgh 1904 map showing both these addresses (J.P. Hunter not named on map) current photo from Allegheny County Assessment site house built in 1905; 7 bedrooms; current market value $125,100
1904	Mrs. Alexander Chambers	5040 Fifth Avenue, near Amberson, Shadyside 1904 plat This is a current photo of a house that was next door to the Chambers home. This block is now mostly condos, but this picture shows 5030 Fifth Avenue, a house that was next door to and built by the same builder as the Chambers house.  Martha Chambers' daughter Olivia Chambers Warren several doors away lived at Fifth and Morewood Avenues,  site of a modern condo today.
1923	Mrs. Olivia Chambers Warren	Corner of Fifth Ave. and Morewood.  1923 plat;  Alexander Chambers property is occupied by N.C. Powers.
1912-1922	Arthur Hamerschlag	4040 Bigelow Blvd.