Troi's character was thwarted in a number of ways. For one, if she was too perceptive, it would kill a whole bunch of plots. I imagine that's why they made her an empath and not a full telepath, but even with reading emotions she never said anything the actors didn't make obvious. "I don't want you here! Get away from my planet forever and never ever come down here!" "He's hiding something." No shit, counselor. The other problem is that they gave all the cool practical psychology stuff away to Guinan. If Troi had even half of Guinan's scenes of clever interactions with the crew, we'd probably think of her as an exceptional psychologist, but they didn't.
He's got SOOO many plates spinning! He's very busy being the driver of the entire plot of a great big saga. There's a lot on his mind.
What have you done today, Deanna? Eating a fudge sundae doesn't count.
To step out of the bit for a moment, when people criticize Troi, they're really criticizing the writing. This character is there to look good and rarely gets anything meaningful to do, and when she does, it's almost always redundant or superfluous to the situation. Marina Sirtis deserved so much better.
Force powers are vague psychic/mystic stuff. We see Vader sense Kenobi, and he can tell that Luke is strong with the force when he is focusing on him. And there's other stuff like sensing Alderaan blowing up or things happening in other places and times (aka literally anything the plot wants the character to see). But the rules just really aren't clear, especially in the original trilogy. There's no indication given that Vader should be able to sense that someone is related to him, nor would he be able to pull it from Leia's mind since she doesn't know either. If anything, he should have sensed the millennium falcon coming in to cover Luke during the trench run, that seems like the more obvious thing to be able to detect.
Troi has empathy, which is a much more clearly defined concept. And while they stray from that sometimes by letting her sense danger or other nebulous generalities, we do know that she should be able to sense emotions, intentions and honesty vs deception. That makes it stand out when the script seemingly forgets that she should be able to sense lies, deception, and malicious intent. Conman pretending to be a researcher from the future lies in order to steal from them and she can't tell that he's a fraud. The staff at a party are getting ready to grab weapons and take them all hostage, and she doesn't notice. These are situations that call for things that are well within her established skillset.
I like cum towns take on that character. Basically star trek fans are so autistic that they introduced an empath character to explain emotions to them.
two: even if he was how is empathic reading supposed to tell him she's his daughter? it's telempathy, not remote gene testing. it isn't like leia was feeling familial affection for the guy.
Vader didn't even know about Leia until Luke leaks it in RotJ. During the Vader/Luke duel is the first and only time Vader acknowledged Leia. Luke's thoughts turned to her during that fight. Vader saw that "weakness", the attachment, and he leapt on it. And it worked (for a moment).
Now it's possible Vader had a rough idea of her existence near the finale of Empire. Luke calls out to Leia. Leia is with Luke when Vader calls out to Luke. I expect Vader was too distracted to notice Leia.
Back to A New Hope. Vader doesn't suspect anything until Obi-wan shows up on the Death Star. Why is Obi-wan here? What is he doing? Then he just disappears? Something about the crew he arrived with is suspicious. Then during the Death Star trench run. He is focused. Vader can sense something. Vader can sense something that can not be. Obi-wan has a Padawan? Why now? Who? Then Han Solo fires at him. Vader should have seen it coming, but he was distracted.
Sooo! Vader seeing Leia opening? He just had no idea.
It's not your empathic abilities, Troi. It's the amount of leading question and interpretations you barrage your clients with that leads me to the conclusion that... well... you are a little shit at your job.
Star Wars is basically a more accessible version of Dune. In Dune people had precognitive abilities that would allow them to predict the future. Problem is if someone else can foresee the future one person is reacting to what they predict the other will do, but then the other changes what they'll do based on what they predict the first person would do. So it results in kind of a stalemate. Two people with precognitive abilities can't predict each other's actions. Or the actions of those under the other's influence.
So the Sith's abilities are weakened by the presence of a Jedi and vice-versa. Leia's ability with the force (whether she knew she had them or not) prevents Darth Vader from sensing much about her other. Also the Sith's abilities wouldn't be effective in predicting the actions of any rebel following Leia's leadership.