from wikipedia: an American playtester working for Capcom reviewed the content during the localization process with one of the Japanese designers, and objected to the protagonist hitting females. Akira Yasuda pointed that the "female" enemies were actually transvestites. and im not sure about their relationship^^
I found their story somewhere in the net. It says that the two girls (yes, GIRLS!) grew up together in an orphanage. Roxy, being the younger of them, took the more mature and independend thinking Poison as her rolemodel and even started to dress like her. They are very close to eachother, but it was never explained if they are just like sisters or if they are even closer. Now that Poison teamed up with Hugo Andore, Roxy's whereabouts are unknown. A rumor says that she died in the story of Final Fight 1, but form me that's to sad to be true.
P.S. I love it when bad girls turn out to have a soft side.
I searched long, but can't find it anymore. The best I could find is here [link])on her Wikipedia site, under "In video games". Btw: This other site said that Poison and Roxy became fighters because their only alternative would have been becoming prostitudes.