I still think Vader and Palps were each vying for Luke to become their "right hand man".
Kinda. The interesting thing about that scene is that there are three distinctively different agendas all at work at the same time.
Palpatine is basically having a playoff. The idea of Vader turning Luke and those two fighting him isn't really a possibility to him. His overconfidence is his undoing. To Palpatine, he's thinking "These two will go at it. And whoever wins, I turn." Either way, he's in charge. He doesn't see it any other way. This is just Skywalker Playoffs to him.
Vader is thinking "I have a kid! I have a REAL family! I can..I can rule the galaxy with him. I can give him something! Give him my power! We can share in this power" he's suddenly mixing his raw ambition, his hunger for power, for domination, with his long hidden parental instincts. He's thinking he might be able to rule with this kid, but on the other hand, he knows how powerful Palpatine is, and he's got questions about Luke's fortitude. And if Palpatine takes him, or if Vader kills him, then he wasn't worthy of his name anyway. He'd lived this long without him, right?
Luke is trying to turn VADER. Which neither one of them will think happens.
Palps is trying to turn Luke against Vader
Vader is trying to turn Luke from the light.
Luke is trying to turn Vader back.
Palps doesn't care who wins, really, either one will be a Sith
Vader wants Luke to turn, but is so indebted to Palpatine that losing Luke is just academic theorizing at this point.
Luke wants to turn his father and kill Palpatine.
There's nothing about this sequence that is really simple. And it gets even more complicated after certain things are revealed in Episode III.