Why does it seem like it never occurred to him that Vader might react badly to seeing his son being brutally tortured to death in front of him? Why have Vader stick around to see that?
If Vader had not known about the existence of his son until his fight in front of Sidious, then I expect he would have dispatched Luke without consideration.
As it is, he had a great deal of time to think about the fact that he had children before he had to fight or watch Luke be tortured. Further, he had threaded the needle, so to speak, and convinced Sidious that 1) he was loyal and 2) to allow Luke to live long enough to make him an apprentice.
Keep in mind that it was family connection and love that Sidious used to bring Anakin under his wing. Sidious knows better than others why the Jedi did not have worldly attachments - including to family.
Sidious knew perfectly well that there is lingering feelings in Vader, he said as much, "I wonder if your feelings on this matter are clear, Lord Vader."
For Sidious this is both a gamble, and a test. On top of his overconfidence - he honestly believed he could best both Luke and Vader if needed - he was pushing Vader to further solidify his master role, and he was risking the loss of Vader to gain a new, better apprentice.
Thus I expect that it was Sidious's belief that he could handle both Luke and Vader if Vader turned. If Vader did turn, Sidious would lose a poor apprentice and a possible apprentice, but he would still have Leia as an opportunity later.
Vader never needed to use his full force capability after visiting the Jedi Temple, and at that point he was using it to protect his family, from his perspective. Since the loss of Padme and any significant jedi opposition, though, he had little reason to exert himself.
Sidious, who had a great view of Anakin's power, realized Vader wasn't half the man Anakin was. He may have assumed that the decrease in power was due to his physical injuries, constant pain, and constant force exertion to keep himself alive. He may have assumed, even, that Luke might be more powerful, but was certainly not well trained.
So Sidious was confident that he could handle both. Further, Vader continued to obey him, attacking Luke, defending Sidious (despite no need to do so), etc. So the chance of Vader turning must have seemed low.
Vader, however, did develop a desire for his son's life and happiness, and when it came down to a decision between Luke and Sidious, he chose Luke.
At that point he picks up Sidious, the lightning appears to go away from Luke, and Sidious looks surprised. Why should he be surprised? Vader's strength is known to him. Why doesn't he attack Vader?
The answer is: He can't.
Vader is not only able to lift him like a doll, but is actively using the force to redirect Sidious's attack. The power Vader uses is enough to overcome Sidious's attack, and this is what is surprising - the powerful Anakin Skywalker is still inside that suit - and now he has a reason to use the power that hadn't been exercised since he entered the Jedi Temple to do terrible harm to protect his wife.
Vader, alone, was more powerful than Sidious.
It wasn't that Sidious didn't consider that Vader might turn against him. It was purely that Sidious believed himself to be stronger than Vader.
In the scene where Luke is being shocked, the fight is over, Luke is defenseless, and the Emperor is literally laughing as he is doing it.
He doesn't seem very focused in either case.
– Wad Cheber Apr 06 '15 at 23:39