Everytime a Batman and a Catwoman crossed paths, it wasn't a traditional hero versus villain encounter. Underneath their conflicting values and beliefs was a romantic tension simmering. If only the Queen of the Cats walk the path of redemption on the side of justice like her Dark Knight opponent. In fact, on Earth-Two, this happened when Selina Kyle grew tired of crime and helped the caped crusader shake of the influence of Scarecrow's fear gas. From the marital union came a daughter, Helena, who would assume the mantle of Gotham's protector as the Huntress after her mother'd death. Shortly thereafter, while visiting Earth-One, she encountered that world's Catwoman who was still a criminal, albeit in her last case as a felon. Then that Selina would finally embrace her Knight in Dark costume, and would date his alter ego Bruce Wayne on-and-off for years. Although not married, they're love would never die.
Not to be outdone by their mentors, the sidekicks of the Batmen also found love in the form of their fellow crimefighters. While teenage Earth-One's Robin knew of the young adult librarian Barbara Gordon and her alias of Batgirl from a distance, the age roles were reversed as an adult Robin of Earth-Two met Helena Wayne when she was but a baby in the arms of the Wayne family. Although he and Helena were surrogated siblings, not truly growing up together but nevertheless in close contact, when a then forty year old Dick Grayson reaquainted himself with the now attorney Helena Wayne aka the Huntress, he found that she had what he was looking for in a love interest. However, the familial connection proved an obstacle, one which a now adult Robin didn't have with Batgirl. However, she could never take the once boy wonder serious enough to forment a true relationship beyond friendship.
In the lives of the Batmen Family, romance rarely reconciles with the rough road of its members.