Darth Vader might have had doubts about Palpatine, however, the Sith Lord made no attempts at murdering the Emperor until Star Wars: Return of the Jedi when he saves Luke from the hands of the powerful villain.
Why’d Vader wait so long to turn against Palpatine even after learning the truth about what happened to Padme?
According to Screen Rant, the answer lies in Star Wars Legends. The novel Dark Lord: The Rise of Darth Vader tries to explain why Vader refuses to betray Palpatine until Return of the Jedi, saying that despite having the strength and capability to kill his Master, the Sith Lord wasn’t in the right psychological state to ever do so.
Had Vader managed to kill Obi-Wan on Mustafar, he would have had the confidence to try and do the same to Palpatine. However, Obi-Wan defeated Anakin Skywalker, and the battle left him severely wounded. Not only that, but Anakin’s head wasn’t in the right place.
Star Wars creator George Lucas once told fans that Vaders/Anakins abilities weakened after receiving all those injuries, and so he had become less powerful than the Emperor. Before he had been defeated by Obi-Wan, Anakin had the potential to become twice as powerful as Palpatine.
Weakened in body and spirit, Vader then dedicates the rest of his days serving the Emperor. It isn’t until Vader finds himself betrayed yet again by the Emperor when Palpatine orders Luke to kill him and then sees Palpatine torturing his son that Vader finds the strength to do what needed to be done – putting an end to the Sith Lord.
The Skywalker saga is available for streaming on Disney+.