sidious takes this fairly easy. luke was nowhere near strong enough to fight him, or resist the dark side. as powerful as vader is hes no sidious. sidious takes out vader with lightning, beats down luke like a schoolgirl, taunts him, makes him angry and and makes him his new apprentice. or just kills him.
They obviosuly wouldn't go to sidious right away they would make a plant first and Vader would teach luke alot of crap.
Vader could also probably Block Sidious' lighting easily, and while blocking it he would walk up to sidious and probably cut off his arm. Then sidious would probably do the same with mace windu "Luke don't you see how cruel your father is, save me and I can make you the new Vader, don't let him kill me!!! and i can save your friends!". Then Luke starts having tears out of his eyes. Then when Vader tries to finish him, sidious would be like please don't, PLEASE DON'T! IM TOO WEAK!!!. Luke appears right beside Vader slices his arm off and then sidious would shock him until his wires in his robotic limbs expldoe killing him.