I finally figured out that picture mystery today. (I asked my grandfather). (Note: post #1 and post #2). The "great grandmother" is Carmela (DeCosmo) Boccamazzo (my great great grandmother). On her lap is John Bocamazo or "uncle John". And the older boy or "grandpa" is Joseph Bocamazo (my great grandfather), Carmela's oldest son.
So I was completely wrong on who was who. I thought it was the Vaccaro's. And I found out who wrote that information on the back of the photo. It was my mother. Since I know who wrote the information, now everything makes sense to me.