In the original 1928 German production, Lotte Lenya played Polly... and she sang "Pirate Jenny" - which has nothing to do with the character Jenny Diver (the whore) in the show. Weill liked the name Jenny, among other American names, and used them a LOT. When the show came to the U.S. in the 1950's production off-broadway (that was actually the second U.S. incarnation - there had been another NY production and that was just like the 1928 German one too), it starred Charlotte Rae as Polly, Bea Arthur as Lucy, and Lotte Lenya as Jenny Diver. Because Lenya was a great song-interpreter and people loved her singing the song "Pirate Jenny," and because she was Weill's wife, she was given the song

That is where the confusion over who the different Jenny's are comes from.
As for the song itself, it stands alone perfectly well. I would just interpret it your way and infuse it with your own power and emotion... if you are performing the song, then you must relate to it somehow :) Go with that! Break legs at your performance.