People in general are really bad at reconsidering life-defining events under a different light, impulsive people most of all, so it's not out of character for Vader to ignore any instincts that tell him there's a connection between him and Leia.

Vader could likely sense that Leia had some latent Force Sensitivity, but so do a lot of people. The inquisitors only cared if they were former Jedi or Jedi in training.

He also didn't realize Luke, whom he almost killed at the end of the movie, was his son either. At least not immediately.

Since Luke still called himself "Skywalker", it was pretty easy for him to put 2-and-2 together after the Death Star event. He had to read Luke's mind on the second Death Star to figure out that he even had a daughter (Anakin did not know Padme was having twins, so he never bothered to search for another child after Luke) and even then he still doesn't know it was Leia Organa, he only refers to her as "your sister".

Obviously the precognition that comes from being an adept user of the Force doesn't allow you to simply pluck knowledge from thin air.

Yeahhhhhh see there’s your problem. You’re taking Star Wars lore too literally. Don’t you know you can’t take every little thing Star Wars adds and assume its actually supposed to make any sense other than “this sounds cool”?

/s, but also not really

Yeah I didn't say it was a good suggestion, just that it was better lol.