Batman gets really jealous when Catwoman returns in Batman 69 (Feb/March 1952).
Finger, Schwartz and Paris relate this tale, in which cat crimes begin once again in Gotham. But this time Catwoman is not the one behind it, a new guy, the King of cats (also called Cat King) is the one behind it.
Batman and Robin question Selina Kyle to see is she knows anything about the man, and discover that she does, and it receiving flowers from him. Batman gets really upset about this.
The King of Cats really does seem to have a romantic interest in Selina. The little hearts emerging from him really can’t be read any other way. He wants her to return to being Catwoman, and work alongside him.
Selina is clearly torn. Batman gets even more upset when she lets the King of Cats get away from him.
But then it turns out that the guy is really her brother Kyle. Which makes sense of much of the story. Except those little floating hearts, which are now really creepy.
Chronologically, the next appearance of this Catwoman is in a Brave and the Bold story in the early 80s. The next actual appearance of Catwoman is a couple of years down the road. Karl Kyle does not, so far as I can recall, return, although I do believe he gets mentioned at least once.