We know that Anakin is power mad, by his statements during his various temper tantrums in AOTC, which may or may not have been influenced by Palpatine's alleged" guidance" behind the scenes (it's mentioned but we never actually see any of this mentoring or what was said or done). When Anakin was a child he had dreams of becoming a Jedi Knight and freeing the slaves of Tatooine (which he never did). Perhaps his dreams deferred, combined with his delusions of grandeur (thinking he was "the chosen one") and desire to have things his way (have a relationship with Padme, despite its being forbidden by his Jedi vows) and to have her live rather than die (though this was all started by his visions of her death, which turned out to be self fulfilling prophecy).
I agree, if I were Vader my first thought would have been to kill Sideous for lying to me about these supposed powers. Perhaps the powers were really unbelievable (even before Palpatine revealed he didn't actually know "the secret" and they apparently never found it) and Anakin just deluded himself into following this path as a way to achieve greater power than the other Jedi whom he feels don't trust him or appreciate his talents as they ought to.
Anakin may be depressed in that everyone whom he ever cared about or cared about him is now dead or cut off from him forever (Kenobi & Yoda, whom he has to know are alive at least at the end of ROTS) by his own actions or acquiescense. He may feel that since his friends are all dead or alienated, his only friend is now Palpatine. He may fear that Sideous is too powerful, but Anakin's delusions of grandeur I would think would make him go after the Dark Lord. After all, he came up with the idea of overthrowing the Emperor and ruling with Padme at his side in his speech on Mustafar earlier.
Perhaps he just thought "well it was MY FAULT" and chose to ignore the fact that Palpatine goaded him into throwing in his lot with the Sith in order to solve his personal problems.
Could Anakin have feared reprisal if he'd told Palpatine to shove it? That Palpatine would reveal the fact that he was secretly married and had ambitions beyond his Jedi Knighthood? Maybe there was a fear of blackmail here, but it would have been nice if we'd seen it, to show that Anakin felt trapped. Instead just willfully goes along with the conman and when it's obvious that he's been conned, he just drops it and stays with the conman for the rest of his life supporting him. Oh well.
While Anakin is definately an impulsive character in the prequels, perhaps Lucas intended to model him after MacBeth, a lot of talk, little action, and poorly conceived action at best. He never freed the slaves or saved his mother, he never tried to overthrow the Emperor (well until the very end when it wasn't for the reasons he'd originally intended and again seemed an impulsive but for once selfless act).
Maybe Vader is suffering from some form of Stockholm syndrome or something. I don't know. Otherwise we're left with some weird Dark Side voodoo that makes it all logically make sense. I think by this point Anakin is a psychopath and its very hard to examine all his actions rationally and come up with something that isn't contradictory (that is not to say that humans can't be contradictory, it's just harder to figure him out as a character, unless Lucas wanted to deliberately make him hard to understand).
For plot reasons, Vader had to stay with the Emperor, but beyond that, it's speculation. I wouldn't be surprised if some of this is pursued in the EU literature though, but whether or not those explanations will be satisfying remains to be seen (I only read the ROTS novel once and I've already forgotten a lot of it).