Revenge of the Sith
Darth Vader and Obi-Wan are fiercely duelling on Mustafar, Padme has been Force Choked and is lying on the Mustafarian landing platform wounded, and the entire Separatist Council lay dead in the main control room just across the way.
As Battle of Heroes plays in the background, Vader and Obi-Wan's fight leads them to the same cliff where we see Vader lose his remaining limbs and gets severely burnt a la Revenge of the Sith.
But what if that scene played out just a bit differently? What if Vader didn't miscalculate Obi-Wan's "High-ground" advantage, killed the bearded Jedi Master, and took his lightsaber? While on Coruscant, Yoda defeated the Sidious in the Senate Chamber and cuts him down. What does this mean to the galaxy far far away...?
Schism within the Galactic Senate
With Palpatine defeated, Yoda would have to escape the Senate Chamber from Clones and Senate Guards loyal to Palpatine. He would escape by leaping into Bail Organa's speeder, but this time Yoda wouldn't flee to a swamp world, he would work with Organa to restore the Republic before it was too late and Vader returned to Coruscant. Yoda would begin meditating in preparations to confront Vader.
Bail would call in an emergency meeting of the Loyalist Committee, the vocal opponents of Palpatine's reformations, and begin working to make an interim government.
However Mas Ameedda, Vice Chairman of the newly formed Imperial Senate, was the first person in the pecking order to ascend into Palpatine's position as Supreme Commander and would have full control of the Clone Army until Vader came back from Mustafar.
Bail, Mon Mothma, and the rest of the Loyalist Committee would begin contacting all the members of the Petition of 2000, their loyal supporters and worlds, and the media to try and sway them to their cause by getting the truth to the people that Palpatine was a Sith Lord and the galaxy was played.
Yet Mas Ameedda had the support of the military and those loyal to Palpatine. Ameedda would have the 501st begin to occupy the streets of Coruscant and the Senate, and send out arrest warrants for the members of the Loyalist Committee calling them traitors and murderers. He would release security vids to the media from inside the Senate Chamber showing Yoda killing Palpatine and of Bail assisting him in escaping. This would solidify Palpatine's previous media statement and speech that "The Jedi hoped to unleash their destructive power against the Republic by assassinating the head of government and usurping control of the clone army" and the naive populous of Coruscant who voted Palptine into power in the first place would eat this up.
Public demonstrations pro and anti-Empire would begin to form across Coruscant and this would be the beginning of another Schism within the Republic.
Vader Returns to Coruscant
Vader would rush to Coruscant with a wounded and pregnant Padme. When Vader reaches the urban planet, he would ignore all the drama in the Galactic Senate and immediately head to Emperor Palpatine's Surgical Reconstruction Center to have Padme treated by the best medical droids in the galaxy. Padme would die during childbirth and the twins would be in Vader's arms.
This is where Yoda would come and confront Lord Vader.
Since Vader's Force power would not have diminished as drastically as they did when he was "more machine than man," he would have the full power of the Force to draw upon. Vader would be emotionally unstable and blinded by rage for his wife's death and these emotions would fuel him. He would unleash his full dark side potential and overwhelm Yoda.
The battle between Vader and Yoda would be long, but Yoda, who had just witnessed the deaths of thousands of Jedi and just defeated the most powerful Sith Lord of all time after a gruelling battle, would be weak and emotionally drained.
Vader would defeat the Grand Master by using Force Lightning of such enormous power that Yoda would barley escape with his life. But he wouldn't escape without saving one of the twins from a life of dark side training. Distracting Vader with a sudden surge of Force enegery, he would flee with a baby Luke and leave Vader in a fuming rage.
Vader, now consumed with rage and hate, would return to the Senate and slaughter Mas Ameedda. He would claim the throne, take the red lightsaber crystal from Sidious' blade, and address an emergency meeting of The Senate as their new Emperor.
Vader would then order the 501st to gather up any Loyalist Senators and have the Clones fire upon the crowds of protestors and supporters of the Loyalist Committee that had gathered around the Senate. The captured Loyalist Senators would have then been executed.
Master Yoda, Organa, Mothma, and the surviving members of the Loyalist Committee would flee to Corellia, where Garm Bel Iblis would agree to shelter Organa and the Loyalists from Vader's navy and armies. The Corellian Sector was an unallied, heavily fortified, isolationist sector safe with it's own organized military.
Darth Vader would have a lot of work to do. Since Sidious was killed before the Empire was fully established, Vader would have to complete the process of turning the Republic into an Empire. Vader was not as charismatic and politically experienced as Sidious and building an Empire would be difficult for him.
Vader would abolish the Senate in an act of arrogance and form The Imperial Advisory Council made up of Tarkin, Yularen, Isard and other trusted top Republic-turned-Imperial officers. This council would be key in helping Vader take control of Coruscant and the galaxy. They essentially become the decision makers and the real minds behind the Empire.
Vader would be a ruthless Emperor ruling through fear, but even though he believes he is in charge, he would eventually become the unknowing puppet to the Advisory Council.
With Palpatine's death, Vader's training as a Sith would not be complete and he would become obsessed with finding ancient Sith training materials such as holocrons and texts so he could learn all elements of the Dark Side and even attempt to bring back Padme.
Vader would also be obsessed with the safety of Leia. He would train her to become a powerful Force user as his Right Hand and hoped that she would rule the galaxy alongside him.
Armed Rebellion Begins
While Vader attempts to create a Empire, Organa would do the unthinkable. Since the Loyalists would be left with no choice but for military action against the ruthless Emperor Vader, Organa would meet with the Separatist Congress on Raxus, the last fortified Separatist Sector in the galaxy and talk about the formation a treaty between the tattered Confederacy of Independent Systems and the Loyalists.
The Separatist Worlds would currently be invaded and bombarded by Legions of Stormtroopers occupying Separatist planets with ease since the droid army had been deactivated. Some Separatist militias and non-droid armies would still fight, but most would be confused and in chaos.
Many leaders of the Separatist would be war-weary and would be hesitant to join a cause that's end goal was to see the reformation of the very Republic they sought to destroy, but many of the Seperatist leaders wanted revenge and still wished to fight.
Former Confederacy Leaders such as Rogwa Wodrata, Sentepeth Findos, and Gizor Dellso along with Loyalist Leaders such as Bail Organa, Mon Mothma, and Garm Bel Iblis would sign the Treaty of Corellia and form the Alliance to Restore the Republic officially declaring war with the young Empire.
The Geonosians would soon find a way to reactive half the droid army and navy and new factories would open across the Outer Rim. Across the Rim Worlds, many citizens would be recruited to fight against Coruscant.
Vader and the Council began taking the war to this new guerrilla army and the Rebllion began.
A New Hope
Yoda would train Luke to become the New Hope of the Galaxy on Dagobah hidden from a vengeful Vader. While Vader would train his daughter Leia to would grow up into his Right Hand and his enforcer.
Luke would be a key member of the Rebellion as a young Jedi with proper Jedi training using Obi-Wan's lightsaber. He would be part of a strike steam sent to capture the stolen Death Star plans and he would stash them in Artoo. A dark side Leia would be the one who boards the Tantive IV not Vader, captures Luke, and orders the Stormies to find the droids with the hidden plans...