The premise is this: during one of Unalaq's early attempts to open the portal, he gets Darth Vader sucked in. One thing leads to another, and in addition to killing Aang, King Kuei II, and Sokka, along with almost the entire original Metalbender PD, he beats up Katara, Zuko, and Toph, along with all of their children before finding the portal again. He vows to return one day, and since Sokka's space sword was the only thing that could withstand a lightsaber, Korra is taught how to use it.
Everything else goes the same until S3's ending, where Korra breaks free and, after defeating Zaheer, he stabs her in the foot with a dagger, before opening a portal the same way as Unalaq, and pushing her in. Mako jumps in after her before the portal closes and Zaheer is captured. Mako cuts off the infected foot before burning the wound closed. They wind up at an isolated Imperial base that treats their injuries and they learn Korra is about three weeks pregnant. Before they can talk, the base is besieged by ugly alien barbarians out to kill everyone. After fashioning a makeshift peg leg, Korra and Mako join the battle and are instrumental to victory, with Mako being injured because he was protecting Korra.
Since they are all they have in this strange new world, they resolve to stick together no matter what. Shortly after flying out with the rest of the Imperials, they meet Darth Vader, who reveals he only wants to talk. Normally, neither would consider it, but with them in an unknown environment, with two children on the way to think about, they listen to Vader's side of the story, where he was attacked by bandits and things just escalated from there. Both are reluctant to believe him but don't see another way out, much less home, so they take his offer to join this Sith Warrior program he and the emperor have just created.
Because Vader is utterly honest with them, from his point of view, and showers with wonderful accommodations for them and their children, Korra gradually comes to agree with what he has to say, while Mako reverts to the pragmatist with a heart that he was in the backstory. Korra also appreciates how the Imperials, such as the ones she and Mako saved, praise her instead of the Avatar, and when she hears the first few lines of the Sith code, she doesn't think it leads to selfishness, she thinks of how passion for bending allowed to learn the first three elements so fast, and how her passion for Mako and desire to protect him from Amon unlocked her air bending, as opposed to the inner peace that Tenzin and others argued for. As she cannot talk to the past Avatars, she can only judge Vader by his actions, and he appears to be much like her. Given her experiences with the Red Lotus and Equalists, she starts seeing the various Rebels as crazed radicals to impatient for change or as selfish bandits who want limitless freedom without responsibility or consequence. Raava and Vaatu are the gods of order and chaos, which many confuse for good and evil, so Korra also thinks she is doing good. Eventually, with Vader's help, she manages to talk to Jinora through that psychic bond of theirs.
Though she doesn't know how to get home, the news she is alive reassures the people she and Mako love, though Raiko and others dismiss it as a little girl seeing what she wanted to see.
Interestingly, she also changes Vader, as he comes to think of her as his ideal daughter despite his attempts to stay unattached, along with acting as tough but fair as opposed to being civil but tyrannical, blurring the line between acting and being. Later on, when she tries water healing on him, she admits she now has a third father in addition to Tonraq and Tenzin. Eventually, she finds Elementia (because what else can I call it) but has to destroy a pirate fleet looking for an easy score. She lands alongside Vader, and meets Kuvira and Baatar, eventually convincing them to start working with the Empire to protect the planet, with part of the deal that she be trained via holo call in the ways of the Force.
She and Mako go back into space as there is an ancient evil stirring close by, and while they don't meet with the people they love, they have the Imperial expedition force, including the ones they first befriended upon losing her leg, surveil them and secretly implant trackers within them. Kuvira tells the story of how the Empire stopped a pirate fleet, showing alien bodies and giving journalists a ride into space to prove her claims, omitting Korra and Mako's involvement, and how she is working with the Empire now, dismissing the caution of many leaders as they greatly accelerate her campaign, though others are forced to acknowledge the possibility the Avatar is somewhere out in the unknown. In addition, the Avatar division, as I will call the Imperials present there, decide the best surprise homecoming present is to purge the Red Lotus in all its prisons, along with various likely agents across the world, though they resolve to take Zaheer alive so Korra can kill him personally. But before they can, he is broken out along with the others in his specific prison by a crime syndicate that has suffered from Korra and Mako's interference, which also kidnaps Korra's mother and numerous other people, even as the rest of the purge goes off without a hitch.
As the world leaders confront Kuvira in the capital over what just happened and her alliance with this mysterious empire, she reveals Korra's involvement. Meanwhile, as the ancient evil is defeated, Korra rushes after the transport with her mother and other loved ones in a starfighter, as Mako and Vader aren't in a position to join her. Disabling the ship and destroying its fighter escorts, she boards it, setting up a diversion so she can enter from another side and catch the gangsters off guard. After killing the last gangster, she tearfully reunites with them and heads home, with Mako meeting them there. Eventually, everyone meets Darth Vader and are shocked to learn that is who Korra is trusting but Korra dismisses their concerns and is more focused on the renewed Red Lotus threat.
Let me make one thing clear: I am a Makorra shipper, Korrasami makes no sense, and I will not be shamed or bullied into saying otherwise. I have also posted the first three chapters and are working on the fourth.