I think that Vader and the Emperor know Obi-Wan survived, I mean Anakin has to know the last thing he saw before he fell in the lava was Obi-Wan. And it's clear from the lines in ANH that it is common knowledge that Obi-Wan survived. Tarkins tells Vader that "surely he must be dead by now", implying that he must have died since the great purge and before their conversation on the Death Star. Then, during the duel, Vader tells Obi-Wan he "should not have come back." Again, implying that Vader knew that he was out there some where.
What this means to me is that Anakin and Palpatine knew that Obi-Wan was alive, but MAYBE not Yoda. They simply considered him(Obi-Wan) no threat.
I don't believe Vader knew that his children were alive. I'm sure both he and Palpatine assumed they died with Padme. Anakin might not have known she was pregnant with twins, we'll see in the movie(but, from ROTJ we can assume he does not.) What this means is that once Vader senses the force in the pilot that destroys the Death Star, he knows something is up. We also know that Vader has killed Obi-Wan by that time. We also know that Vader says that Kenobi IS on the Death Star and that the Force is with him. As we know, after Anakin's(the chosen one's) fall/"death" at the end of the duel in ROTS, no more force sensative beings are born and that the light sid eof the force exists only in teh world of the dead with the fallen Jedi. This has to raise Vaders eyebrow...or whats left of them. He knows Obi-Wan is dead by this point...so this other HAD to have been born before the fall. This is where the wheels start to turn in Vaders mind.
So, to sum it up: Vader knows Kenobi is alive, before he kills him.(As does Tarkin and the Emperor) Vader knows, after the trench run and destruction of the Death Star, that there is a new force sensative being in the galaxy...and that he is strong. He knows Padme is dead, and that he is at fault. He MAY think that Yoda is dead. He will eventually find out that the force died when he fell to the dark side and will, at his death, know what Kenobi meant when he said "if you strike me down, I will become more powerful than you can possibly imagine"....by becoming a force ghost himself.