Hi Bill,
I don't have much info for you, I'm afraid. I have 3 Trentadue's in my files, all female and from 3 different towns.
Maria Carolina Trentadue Jun 28 1844 Carbonara, married Savino Menolascina 1873 in Carbonara.
Filomena Trentadue Apr 9 1866 Triggiano, married Vito Tunzi 1887 in Triggiano.
Domenica Trentadue, born 1885 in Modugno, married Giacinto Ardito in 1907 in Modugno.
In each case, the Trentadue married into one of my liens, so I don't know who the parents of the Trentadue's are.
What other surnames connect to your family that are from Bari? I might be able to narrow down your town using the other surnames that your Trentadue family married into.
Thanks
Dan Niemiec