Much of what is known of Kathy Kane's life as Batwoman is inferred from Earth-One counterpart, of whom there is extensive documentation.  How much exact overlap exists between the two remains unclear.   It is most likely that the earliest casework overlaps extensively with some degree of drift as their careers were influence by different factors in different timelines.  Two cases of note occurred within a year of her debut.  In the first, an escaping criminal doffs his cowl while running through smoke and when hit in the head develops amnesia. Batwoman assumes the criminal, Curt Briggs, must be Batman as she knows him as a local physical fitness instructor and not a crook.  Coincidentally, Batman has sprained his angle and must stay out of sight, further convincing Kathy that Briggs must be an amnesiac Batman.  As Briggs memory returns he returns to crime, ultimately captured by Batwoman and Robin when Batman stages an appearance hiding his injured leg.  Afterwards Kathy retires again (Batman #105).  A few months later, Bruce Wayne goes undercover to flush out a criminal conspiracy in prison for Commissioner Gordon but ends up accused himself.  He is slated for execution until once-more un-retired Batwoman and Robin save the day (Detective Comics #249).

After this case, it appears that Batman is more accepting of his new colleague.  She is known to have likely participated in several cases on Earth-Two best described on Earth-One, including a battle with the Firefly (Batman #126) and another with the Spinner (Batman #129 and alluded to in Brave and the Bold #182).  She was known to be active at least as late as 1955 when the Scarecrow went on a crime spree through Gotham.  In one episode, he managed to dose Batman with a potent amount of his fear gas, activating an intense autophobia, a fear of being isolated.  So intense was Batman's experience that he began to hallucinate that those close to him like Robin and Batwoman literally vanished.  The spell was eventually broken when he teams up with Catwoman, revealing their histories and finally bonding in a way that opens Batman up to his eventual marriage to Selina Kyle.  Who captured the Scarecrow is not entirely clear (The Brave and the Bold #197).

Once Batman committed himself to Selina's reform and their life together, he distanced himself from other women in his life, including Batwoman.  Sensing the change, Kane gave up the Batwoman identity, married another man and had a family.   Her activities in the '60's and '70's are largely unrecorded.  In 1979, the Batman is killed by Bill Jensen, an agent of a Frederic Vaux (Adventure Comics #461-463).  Some months later, a freak accident pulls the Earth-One Batman to Earth-Two and at the same time, the Earth-Two Hugo Strange returns seemingly from the dead.  Having seized Starman's cosmic rod, Strange goes on a campaign of revenge, throwing Batman's relics such as the Batomobile, Catwoman's Pantherajet and the Spinner's tops into the city.  The Batman of Earth-One and the Robin of Earth-Two combined forces to stop Strange and when the Bat Signal is activated, Batwoman comes out of retirement to investigate.  The three track Strange back to the Batcave where Batwoman has to be blindfolded - Batman never shared his identity with her.  While she and Robin struggle to overcome the reticence to destroy the Batman's memories, the younger Batman engaged Strange directly, convincing the aged and decrepit criminal that what he really longs for his death, causing Strange to turn the cosmic rod on himself, committing suicide.  The Batwoman returns to her normal life as the Batman of Earth-One is returned home (The Brave and the Bold #182).

The final fate of Kathy Kane on Earth-Two is unknown, though she is noted to be a prominent citizen of Gotham City (Who's Who Vol. 1 #2).  Her full history and legacy remains unrevealed.