At what point did Count Dooku find out about Darth Sidious's true identity? Throughout Episode 2 it seems as if he does not realize that Palpatine and Sidious are one in the same. By Episode 3, however, the look he gives Palpatine when he orders Anakin to kill him implies that he knows. When was this revealed? And what was Dooku's reaction?
Count Dooku has known about Sidious/Papaltine for as long as he was his apprentice.
I haven't read the two books that these events span over, so I'm going based off the citations, but according to Wookieepedia...
During Darth Plagueis - which occurs between Episodes 1 & 2:
Palpatine did not reveal himself at that point, unsure of Dooku's true allegiances. However, with the death of his Master Plagueis at his own hand, and the presumed death of Darth Maul at the hands of Obi-Wan Kenobi, Palpatine needed an ally to further his own plans for galactic domination.
During Nute Gunray's final trial out of four tribunals for his role in the Naboo Crisis, Dooku learned from Gunray about Darth Sidious' role behind the scenes in the crisis, to which Dooku then promised to supply this information to the Jedi Order. It wouldn't be until 22 BBY that he would eventually reveal this information to the Jedi, and even then, only to Obi-Wan Kenobi, who would later supply this information to the Jedi Order.
However Dooku's fate as a Sith apprentice was sealed before it had begun, as Sidious had already met the young boy Anakin Skywalker, the supposed Chosen One of Jedi prophecy. Realizing Skywalker's one-of-a-kind potential in the Force, Sidious had already made plans for Skywalker to serve as his final apprentice. As such, Sidious decided to keep Dooku only as a place holder until Skywalker had fully matured, while still using the fallen Jedi's unique talents to further the Sith agenda.
Based on these paragraphs, it can be argued either way whether nor not Papaltine has actually revealed his hidden identity.
But almost immediately following, during Labryinth of Evil, they meet again - this time with Papaltine/Sidious explaining his full plans (minus the part about Dooku eventually being replaced by Skywalker).
Shortly after their meeting on Coruscant, Dooku was approached directly by Darth Sidious. They had a long discussion, and Dooku found that Palpatine's goals were not dissimilar to his own. Despite the recent death of Dooku's apprentice Qui-Gon Jinn at the hands of Darth Maul, Darth Sidious found it surprisingly easy to convince Dooku to ally with the Sith. After seventy years in the Jedi Order, Dooku abandoned his friends and the Jedi way for the dark side of the Force.
Under the tutelage of Sidious, Dooku was renamed Darth Tyranus and became a Dark Lord of the Sith.
He always knew. Joined the dark side, Dooku has. He knew throughout episode 2. When he told Obi-wan about Sidious on Geonosis he was doing two things; 1) he was revealing to Kenobi that Sidious was too clever but was careful not to give too much info. And 2) he was trying to seduce Obi-wan saying 'I know where this guy is. You and I can beat him and take over.' Because that's what Sith do. They deceive each other for their own gain. Deceit and mistrust are his ways now. In any case, that's my take.
No, he knew Sidious was Palpatine. Remember the Jango Fett line "I was recruited by a man called Darth Tyranus on one of the moons of Bogden." Tyranus was directly involved in the planning of the Clone Army. The Army was commissioned by Jedi master Sifo-Dyas, likely under the Force/Psychological manipulation of Darth Sidious and his master Darth Plagueis. The fact that Fett was hired to provide the genetic source for the clones indicates to me that Sidious was breaking the Rule of Two, even when he was still apprenticed to Plagueis. I think it means that Sidious took Tyranus on as an apprentice shortly before he betrayed Plagueis and that Tyranus was involved in that plot. It also means that he has both Tyranus AND Maul as apprentices at the same time.