Because he thought Vader did not kill him on ESB because he felt for his son. I do not think that is so for a moment, because by the same logic Luke thought Vader would not hand him over to the Emperor, and Luke was WRONG.
I believe no spark of anything in Vader was awakened until that final moment. Before that point, Vader was perfectly ready to kill Luke if he had to.
I do believe that in ESB is was merely for recruitment, but in ROTJ, after the talk on Endor, I think Vader felt something different. You can see it in his body language, he's really torn. I think he did want to train Luke because it was his son, but I don't think he had any intention of giving up being Sith until the end of ROTJ. AND WHAT ARE ANAKIN'S LAST WORDS?!
"You were right about me, tell your sister you were right". So OBVIOUSLY Luke isn't wrong if Anakin told him how he felt.
Vader always wanted Luke as his apprentice, getting him in the same vicinity as Palaptine was mainly so they could gang up on and kick his @$$. Everything he told the Emperor was just to stall to give Vader enough time to turn Luke himself. Its the basic Sith mentality that Lucas has spoken of in interviews and commentaries. I don't think it was until ROTJ that he actually started to want Luke around as his SON as opposed to a tool to seize supremecy from Sidious.
As for Piett, he was just a really good and loyal officer, he respected Vader where as the others always sort of view him as an oddity. Like the first guy Vader choked, he was an arrogant little prick who tried to tell Vader what was what so he got choked. Vader did warn Piett "do not fail me again, ADMIRAL". So I'm sure he would have had choked him had he failed again.