Emperor Palpatine sensed something change in Vader, something he didn't like. When he was united with his son for the first time something changed in him, and now instead of wanting to destroy or convert him, he now has paternal instincts.
Palpatine knows Luke is going to be powerful, possibly to the extent that he himself would be a casualty at the hand of a Skywalker. For all that Palpatine could forsee, he did not see everything.
Vader wants Luke to join him so together they can take out Palpatine, Vader will be the new Emperor and Luke his apprentice. Anakin always had a different ideal of how this empire should be run. While a Sith, he was no where near as tyrannical as Palpatine. Palpatine is chaotic evil, whereas Vader is more like lawful evil, by comparison.
Vader told Luke he could kill the Emperor because Vader wants Luke to believe he can because Vader is no longer physically able to do it himself because of his handicaps and limitations. By suggesting to Luke that together they can end this, it was his hope Luke would join his father on this new crusade.
Palpatine sensed a treacherous Vader, but he thought Luke would be manipulitable enough to convert like Anakin was. Palpatine doesn't trust Vader anymore since he met his son.
Aside from that, its just the Sith way of life to expect betrayal from your own apprentice at some point. Sith are power mongers. Unless they are completely broken like Darth Maul and reprogrammed mentally they will have their own agenda eventually when they've learned all they can from their master. Palpatine did the same to his own master, we now know.
Anakin is the chosen one to bring balance to the Force in this instance, by killing Palpatine. Buts he's just as much the chosen one because of the balance he would also bring through his children, and then balance they would bring to a new generation, and so on.
Palpatine was so caught up in his rage of killing Luke that he couldn't sense the man standing right next to him was no longer his servant, has reclaimed his identity and would seconds later prove it.
He suspected Vader, but perhaps figured that if forced to kill his son, it would prove his loyalty because then the bond the two share would no longer have a hold on Vader and his connection with the Dark Side would be perminently cemented and the hidden remnants of Anakin Skywalker would die and cease to be.