Where does the "your" come in? Based on what I've learned so far, I would have thought this was "work with the family"
I mean "la Famiglia" ... http://en.wikipedia.org/wiki/The_Godfather ... It's a joke of words between Famiglia and Cosa Nostra and the "your" of the translation. ; ) Look up, at the first comment : "Lavora con la tua famiglia"="Work with your family!" . Is not necessarily his family, may be the family of another. (Maybe is our family , but here it's not specified)
OK Con la = colla but According http://www.treccani.it/enciclopedia/con_(La_grammatica_italiana)/# it is not longer used.
"col" and "coi" are remaining but they are rare in current speaking