If Vader and Palpatine knew they intended to replace one another, then why all the song and dance about recruiting Luke? Why didn’t Vader just let Luke kill Palpatine in that first instance?
This is something I have also been thinking about lately. I think Vader and Palpatine always knew that they would both want to use Luke to take out the other, but they both didn’t necessarily want to reveal their hand either. For them, it’s like playing a game of chess.
And while I don’t think either of them ever had the intention of ruling the Empire as a triumvirate, even with the existence of the Rule of Two, it hasn’t stopped the Sith from having dark side acolytes before, such as Ventress or the Inquisitors.
But I think after Luke chose death over joining Vader in ESB, Vader no longer believed he could turn Luke on his own. He needed the Emperor, and the Emperor says as much in his first scene with Vader in ROTJ.
And I think Vader’s extreme loyalty to the Emperor in ROTJ is partly because he may not want to reveal his intentions while the Emperor might be close enough to easily sense them. On the other hand, it may just simply be that Luke’s decision to fall to his death over joining his father may have affected Vader’s own confidence in his power. Maybe at this point Vader truly feels what he says about the Emperor, especially after being his servant for so many years, and the events at the end of ESB set him back into that mindset.
But my question, like you brought up, is why didn’t Vader just let Luke kill the Emperor when Luke took that first swing at him? I mean, the Emperor even says that if he killed him, his journey toward the darkside would be complete. My only guess is that Vader knew that it would require more than that to turn Luke, and the Emperor was just toying with him in order for him to initiate aggressive combat. Luke really needed to see that the darkside was power, and he wasn’t there yet.