Vader's plan in TESB...

The problem here is simply that, at the time the OT was made, Lucas considered Yoda (and the Emperor) to be of an entirely different nature to the Jedi Knights:

Lucas: "Also another misconception is that Yoda teaches Jedi, but he is like a guru; he doesn't go out and fight anybody."
Kasdan: "A Jedi Master is a Jedi isn't he?"
Lucas: "Well, he is a teacher, not a real Jedi. Understand that?"
Kasdan: "I understand what you're saying, but I can't believe it; I am in shock."
Lucas: "It's true, absolutely true, not that it makes any difference to the story."
Kasdan: "You mean he wouldn't be any good in a fight?"
Lucas: "Not with Darth Vader he wouldn't."
[...]
Marquand: "The Emperor doesn't have Jedi powers, does he?"
Lucas: "Well, he is like Yoda: Yoda isn't a Jedi, the Emperor isn't a Jedi. Yoda has mystical powers and it's the same thing with the Emperor; he's like the grand priest, but he's not chief of the tribe. Jedi are the chiefs, they are the warriors who go out and fight with their swords. The Emperor and Yoda are the priests who are the spiritual chiefs; they have powers that are much stronger." - From the transcripts of the Return of the Jedi story conference, July 1981

To be honest - this kind of thing is at the heart of every "for and against" prequel argument.
I'd say the above account of the nature of the Jedi Knights, the function of Yoda as a Jedi Master, and their relationships with the Force and the bigger picture of the saga is all reasonably implicit in the original three movies, without ever being explicit.
There is, after all, more to be absorbed from the movie experience than what is explicitly stated onscreen.
But some aspects of the prequels manoeuvre around in that grey area of "we didn't say this couldn't happen... so it could, and can."

Which is why the argument is never-ending.
Something explicit in the prequels undermines what is implicit in the original movies, and no-one can win because one side can never prove what was implicit to begin with, while the other side won't back down because it believes there is no need to even prove something that is not explicitly ruled out.

And yet, in this case, it could all be so simple:
Why do Vader and The Emperor not know/care about Yoda?
Because they have no reason to know/care about Yoda within the context of the OT.
It only becomes an issue when you introduce this:
Vader and The Emperor definitely DO know about Yoda and definitely DO have a reason to care whether he is alive or not.
Ultimately, you can not react in 1980 to something which happened in 1999...