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Rosie was Dorothy's older sister. When Verne Brown and Marty McFly took the DeLorean time machine to September 27, 1944, a civil defense warden caught them trying to break into Verne's father's apartment, and he impounded the DeLorean time machine.
Without a way home, Verne and Marty spent the night at a victory garden in Courthouse Square. Marty was attracted to Rosie, earning him the ire of Sergeant Frank Tannen. While running away from, Tannen, Marty accidentally enlisted in the United States Army. Meanwhile, Verne befriended Dorothy, and soon discovered that when she gets older, she becomes his dancing instructor in 1992.
Eventually, Marty managed to escape Frank Tannen when Verne and Dorothy entered and won a dancing competition at a USO show. Marty and Verne were able to return home to 1991, and Verne resumed dancing lessons with Dorothy, although he was now enthusiastic about dancing.
It's assumed that because she was Dorothy's older sister, she is no longer alive in 1991.