It has to be said, right from the outset, that Beatrice isn't a particularly well-drawn character in the play. That said, she does play an important role all the same. Warm, caring, and unfailingly sensible, she brings a sense of stability to proceedings, an important consideration given the enormous disruption precipitated by the sudden arrival of Beatrice's immigrant cousins Marco and Rodolpho.
It's Beatrice who tries to hold the Carbone family together while everything is falling apart. She presents an idealized image of traditional Italian-American womanhood: strong but at the same time submissive to her husband. Unfortunately, this limited role places severe restrictions on how Beatrice can help avert the catastrophe enveloping her family. At no point in the play does she shape events; in fact, she always seems to be at the mercy of them as Eddie, Catherine, Marco, and Rodolpho engage in an extended power play that ultimately leads to tragedy.
In addition to the tragedy of Eddie's death, there's also the tragedy of Beatrice being able to perceive what's going on and where it might lead but being unable to do anything about it, due to her restricted role as a traditional Italian-American housewife. Long before the tragic denouement, she can sense where things are headed, yet she cannot do anything to stop the course of events.