Yoda and Ben make a big fuss about how important it is for Luke to confront Vader, but they make no mention of him needing to kill the Emperor. Doesn't the Emperor also need to be destroyed to restore peace to the galaxy?
Yoda did acknowledge that Luke would eventually have to defeat the Emperor:
Yoda: Only a fully trained Jedi Knight with the Force as his ally will conquer Vader and his Emperor. If you end your training now, if you choose the quick and easy path, as Vader did, you will become an agent of evil.1
However, they emphasized Luke's confrontation with Vader because Vader was an easier target than the Emperor (the Emperor had defeated Yoda himself, but Vader's connection to the Force was weakened by his defeat at the hands of Obi-Wan on Mustafar). Luke needed to prove to himself that he could confront Vader and survive without turning to the dark side. Only then would he be a full Jedi:
Yoda: One thing remains: Vader. You must confront Vader. Then, only then, a Jedi will you be.2
If Luke finished his training and confronted Vader without turning to the dark side, the rebellion would have a fully trained Jedi on their side to oppose the Empire. This would increase the Rebel Alliance's chances to defeat the Empire, and in doing so help gain allies from systems which wanted to rebel but were afraid to do so. With the help of a fully trained Jedi, the Rebel Alliance could conceivably score victories against the Imperial military and perhaps kill Vader himself. Then, the Emperor would be politically and militarily weakened, and Luke would be strong enough to defeat him.
But that's the long game. At this point, Yoda and Obi-Wan were trying to avoid a scenario of total defeat: Luke was their (nearly) last hope, and if they lost Luke to the dark side they would have virtually no chance to defeat the Sith.3 In that case, the Empire would be even stronger (yet another Sith), and the Rebel Alliance's morale and support would suffer massively -- because the hero of the Rebellion joined the enemy!
Thus, the fate of the Rebellion hinged on Luke's confrontation with Vader. That's why Yoda and Obi-Wan put so much emphasis on it. Luke could confront the Emperor later, once he was better prepared.
Since we're not privy to what Yoda and Obi-Wan saw through the Force, we don't know how they expected Luke's confrontation with Vader to turn out. It's possible they had an inkling that Luke would redeem Vader and then either Luke or Vader would defeat the Emperor, but Obi-Wan seemed to think that Vader was irredeemable (Obi-Wan says Vader is "more machine now than man"). They probably thought Luke would have to kill Vader, as indicated by Luke's conversation with Obi-Wan in Episode VI:
Luke: I can't kill my own father.
Obi-Wan: Then the Emperor has already won.
They thought Luke would have to kill Vader, but he would have to do it as a Jedi rather than giving in to his anger. If Luke did this, he would prove to himself that he could defeat a Sith Lord with the light side of the Force rather than turning to anger and the dark side. Luke would need this confidence as a Jedi against the Emperor, too, so Luke's confrontation with Vader was crucial.
1 Episode V, as Luke is about to leave for Cloud City
2 Episode VI
3 It's true that Leia was another hope, but the situation would be even more bleak if it came down to Leia. If Luke turned to the dark side (either by killing Vader or simply joining the Sith), Leia would have to somehow defeat the Emperor and a young, evil Luke (and possibly Vader) all by herself. And while Luke at least had a crash course in Jedi training from Obi-Wan and Yoda, Leia wouldn't even have that -- Obi-Wan was already dead and Yoda died before the Battle of Endor.
As far as I know, this isn't addressed in the films themselves, and I don't know much about the secondary materials. I will do my best to answer it within the context of the films, and with the least possible amount of speculation.
Last things first, you asked if Yoda knew that Vader would bring Luke before the Emperor. The answer to this question is a definite "yes". From the script:
LUKE But I need your help. I've come back to complete the training.
YODA No more training do you require. Already know you that which you need.
Yoda sighs, and lies back on his bed.
LUKE Then I am a Jedi?
YODA (shakes his head) Ohhh. Not yet. One thing remains: Vader. You must confront Vader. Then, only then, a Jedi will you be. And confront him you will.
YODA Remember, a Jedi's strength flows from the Force. But beware. Anger, fear, aggression. The dark side are they. Once you start down the dark path, forever will it dominate your destiny.
He beckons the young Jedi closer to him.
YODA Luke...Luke...Do not...Do not underestimate the powers of the Emperor, or suffer your father's fate, you will. Luke, when gone am I (cough), the last of the Jedi will you be. Luke, the Force runs strong in your family. Pass on what you have learned, Luke...
Yoda is careful to say several important things here:
- Yoda tells Luke that he must confront his father again. The last time Luke and Vader met, it didn't go very well. Luke was almost killed, and he actually did lose a hand; he learned Vader was his father too soon. In the same scene quoted above, the following exchange takes place, which supports the idea that Luke didn't accomplish whatever it is that he's supposed to accomplish by confronting Vader:
Luke: [visibly in agony] Master Yoda...is Darth Vader my father?
Yoda: [turns away from Luke] Rest, I need. Yes, rest.
Luke: [pleading] Yoda, I must know.
Yoda: Your father, he is. [Luke looks away] Told you, did he?
Yoda: Unexpected, this is, and unfortunate.
Luke: [surprised] Unfortunate that I know the truth?
Yoda: No. [turns to face Luke] Unfortunate that you rushed to face him. That incomplete, was your training. That not ready for the burden, were you.
Luke: I'm sorry.
Yoda tells Luke that, when he does face Vader again, he must not give in to anger, fear, and aggression, or he will fall irreversibly to the Dark Side of the Force. This suggests that the purpose of the confrontation is not to fight him. He is supposed to do something else, something that isn't motivated by anger, fear, or aggression.
Yoda tells Luke that he must not underestimate the power of the Emperor, or he will "suffer [his] father's fate" and become the next Darth Vader. If Yoda didn't expect that Vader would bring Luke before the Emperor, he probably wouldn't have bothered to say this.
So, as far as I can see, Yoda certainly expected Luke to confront Vader and the Emperor, and he made sure that Luke knew the goal wasn't to kill them. What was his goal? He explains it to Leia:
Luke: Then you know why I have to face him.
Leia: No! Luke, run away, far away! If he can feel your presence, then leave this place! I wish I could go with you.
Luke: No, you don't. You've always been strong.
Leia: But why must you confront him?
Luke: Because there is good in him. I've felt it. He won't turn me over to the Emperor. I can save him. I can turn him back to the good side. I have to try. [kisses Leia on the cheek, then leaves]
As this conversation shows, and as I have explained in a previous answer, Luke was supposed to avoid the temptation to resort to violence against Vader and the Emperor, and provide the impetus for Vader to redeem himself. Only by doing this could he become a Jedi.
Obviously, Luke comes dangerously close to failing in his mission, on more than one occasion. First, the Emperor exploits Luke's concern for the rebels attacking the Death Star, and Luke briefly attempts to kill the Emperor. He manages to calm himself down, but then his feelings for Leia betray him, and Vader uses them to provoke Luke into a fight. Luke's response is an incredibly aggressive attack on Vader, which comes to a head with Luke lopping off Vader's hand. Vader is prostrate on the ground, helpless; Luke is standing over Vader with his light saber poised to strike, teetering on the brink of killing his father and falling to the Dark Side. Finally, he sees Vader's stump, looks at his own artificial hand, and realizes that this is the crucial moment: what he does next will determine the future course of his life. The Emperor is giggling with delight, urging Luke to finish Vader off, thus completing his fall to the Dark Side. Luke collects himself (in my opinion, this is the moment when he sees what he must do to achieve his objective), tosses his weapon aside, and says:
Luke: Never. I'll never turn to the Dark Side. You have failed, Your Highness. I am a Jedi, like my father before me.1
Palpatine: [angrily] So be it... Jedi!
Luke refuses to give in to Palpatine's demands and disarms himself.]
Palpatine: [raising his hands toward Luke] If you will not be turned, you will be destroyed! [Fires lightning bolts at Luke, causing him to fall to the floor in agony. Darth Vader gets up and stands next to Palpatine, watching.] Young fool. Only now, at the end, do you understand. [shoots another round of lightning] Your feeble skills are no match for the power of the Dark Side! You have paid the price for your lack of vision! [continues shooting lightning]
Luke: [writhing in agony] Father, please! Help me!
Palpatine: Now, young Skywalker... you will die. [intensifies lightning blasts]
Darth Vader: [looks back and forth at Luke and Palpatine. He grabs Palpatine from behind and throws him down into the reactor shaft]
Vader: Luke, help me take this mask off.
Luke: But you'll die!
Vader: Nothing can stop that now. Just for once, let me look on you with my own eyes. [Luke carefully removes Vader's mask to reveal Anakin's disfigured face underneath.] Now...go, my son. Leave me.
Luke: No, you're coming with me. I won't leave you here. I've got to save you!
Anakin: [smiles] You already have, Luke. You were right. You were right about me... Tell your sister... you were right... [dies]
1 Luke knows that, by tossing away his light saber and refusing to kill Vader, he has already passed the test, and is now a true Jedi.
It is clear, in light of all that has been said above, that Luke had to face Vader and the Emperor as a kind of test. The test was twofold:
Resist the temptation to use his anger, fear, and aggression against his opponents.
Provide the impetus for Vader to redeem himself.
He almost failed to achieve the former, but eventually pulled it off; by reaching the first objective, he ensured that he would also reach the second. His mercy towards Vader was probably the factor that inspired Vader to show mercy towards Luke, and by saving Luke and killing the Emperor, Vader achieved redemption.
Because baby steps.
Luke isn't even ready to confront Vader yet, so the Emperor (who, as we found out in the prequels, easily bested Yoda) was so completely way out of Luke's league at the moment it wasn't even worth introducing the idea into Luke's head.
Also, while not explicitly state in canon, we know that Anakin was the Chosen One, with the prophecy and all. It's not unlikely that Yoda got some sort of a hint off the Force that because of this, confronting Vader was the right first step. Sort of a "I got a really good feeling about visiting Hagrid" thing.
I believe the reason was because they knew anakin would kill the emperor, he was a undercover dark sider, not governed by an agency but by his own emotions. Similar to luke, the character portrays we all have demons but can still be essentially good people who just got a little bit lost on the way.
Would explain the my father is a jedi quote.
I also believe Skywalker men are born to topple empires, whilst the females are born to form new ones. Imagine where a world governed by one entity for so long allowing no change and inevitably leading to give into darker temptations, purely an evolutionary defense to protect itself. Yoda may of known or already experienced it several times before.