The Jedi Council wouldn't want to compromise the Jedi traditions. The main reason why Anakin and Padme kept it a secret was because Anakin would've been kicked out of the Jedi Order since attachment - let alone marriage - was against the Jedi Code.
The marriage, witnessed by the droids C-3PO and R2-D2, was kept secret due to Amidala's place as a prominent Senator in the Galactic Republic and because of Skywalker's membership in the Jedi Order; the Jedi Code prevented Jedi from falling in love and forming attachments such as marriage.
He owed them too much." It seems Anakin simply could not imagine what his life would be like without the structure and support of his Jedi family, and he was quite simply too afraid to let them go.
Then, he would have left the Jedi Order if she asked him to, but instead, they parted ways, and he was never able to fully let go of the regret he felt for the life he could have had. Obi-Wan wanted Anakin to have the married life he never had, and so he resolved to remain silent.
Padme Amidala
Padme Amidala's secret marriage with Anakin Skywalker was one of the biggest reasons he eventually turned to the dark side. His emotions and love for her often clouded his judgment, and sometimes led him to be violent.
However, when they next met in Star Wars: Episode II – Attack of the Clones, Anakin and Padmé's feelings for one another grew into something resembling love, and their wedding at the end of the film solidified their relationship as one of the most important romances in Star Wars history.
Yes, his entire character since then was a self loathing tragic monster who has little reason to care about anything. Betraying Mace Windu instantly made him regret his act of impulse, Padme's death and rejection of his actions later on made it stick.
The film doesn't flinch away from how horrific that act is, especially as it begins the downward spiral of Padme's death. Nonetheless, as she dies, Padme tells Obi-Wan that there is still good in Anakin. Even something as heinous as that couldn't fully break her love for Anakin.
Yes, when Darth Vader turned back to Anakin Skywalker and sacrifice himself to save his son, he dies and Obi-Wan uses the force to connect with Anakin's spirit. In that time Anakin apologizes to Obi-Wan, desperately asking him to forgive him for everything he has done to him and everybody over the years.
They may not know the extent of Anakin's relationship with Padmé, or even that they are legally married, but it seems abundantly clear that Yoda, at the very least, was aware of Anakin's strong attachment to Padmé, and that those feelings were reciprocated, too.
Every time she speaks, he remembers Padmé. Fighting alongside Sabé reminds him of fighting alongside his wife. While that is certainly painful enough, it's also reminds Vader of the man he used to be, a past he had long ago attempted to kill and bury. However, the memory of Padmé via Sabé won't let his past stay there.
It's not shown, but it is clearly insinuated that Anakin killed the younglings. This is confirmed later in the movie when Obi-Wan informs Padme that Anakin killed them. Both are torn apart with hurt and confusion, trying to make sense of something so terrible. How could Anakin do such a thing?
Padmé was well aware that Anakin had committed dark crimes that would've started his fall to the dark side. He even confessed to her that he had massacred an entire Tusken Raider village to avenge his mother, leaving no one alive.
Short answer: no. Her little run-through with Clovis was during her early Senatorial days, before Anakin came along and fell head-over-heels in love with her. Any feelings she exhibited for the former on Scipio were purely out of respect or for business (since he was a powerful member of the Banking Clan).
Many fans of the franchise theorize that Padme Amidala – Anakin's love interest and actual wife – has cheated on him. The theories claim that she had an affair with either Clovis or Obi-wan Kenobi. Both theories are not true.
If Anakin had never fell in love with Padmé, he would've never turned to the Dark Side because it was his fear for losing Padmé and his two unborn children which caused him to be easily seduced by the Dark Side of the Force. It was his fear which made it much easier for Palpatine to manipulate Anakin.
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence. "Sister," the Emperor taunted.
Darth Vader hated Obi-Wan Kenobi because he hated himself. This started when he thought that Kenobi was the one that poisoned Padmé into turning against Anakin when he turned to the dark side. But the truth was that Anakin was merely projecting his own self-hatred toward Obi-Wan.
At some point after his transformation into the armored Darth Vader, Amidala's husband, the fallen Jedi Knight Anakin Skywalker came to visit the mausoleum, stricken by grief and remorse for his part in her death.
To hide the birth of her twins from both Darth Vader and more importantly Palpatine. The fact that Amidala had given birth to twins was a secret known only to a few after her death. The mortician Commodex Tahn used a hologram to make her still appear pregnant during her funeral.
It seems he's deeply disturbed by the fact that she's pregnant. What is this trying to convey? It's not really brought up the rest of the movie - he has visions of her dying in childbirth, but all the while he's happy and excited about his future children.
Originally Answered: After Padme died why did Anakin choose to stay on the dark side? The only reason why Anakin joined the dark side in the first place was to save Padme from dying during her pregnancy. He had no choice after the events of Episode III. He had lost his wife and his friends/comrades in the Jedi Order.
Vader didn't know how Padmé died
The emperor told Vader that Padmé died due to Vader's rage when he used the Force to choke her, as the former Anakin couldn't believe it because he felt that she was alive before he released his hold over her.
After Padme died, Anakin had already fully committed to the dark side. Even if he still desired to do good, his anger had corrupted him to the point of no return.