Note: This is a sort of fusion, with the SW characters/setting set (more or less) to a LOK storyline, but it should be able to stand on its own as a SW story. More explanation (with LOK spoilers) at the end, if you're interested.
Their father killed the Emperor just after Luke and Leia's fourteenth birthday. It was already too late. They'd had years of training at Palpatine's hands, during that early time when Darth Vader—reluctant, but unwilling or unable to defy his master—was busy crushing all opposition to the Empire.
It was not that the twins felt any greater loyalty to Palpatine than to Anakin Skywalker. Quite the contrary. The latter was a careful, pragmatic teacher, and a loving father even outside their training in the Force. He didn't frighten them; they knew he could be dangerous, but only to others, to people who deserved it. Not them; he loved them. As children, Luke and Leia adored him, and even after Palpatine's training had burned nearly all affection out of them, they remained loyal to their father.
They hated Palpatine, and loved each other, in about equal measures. His training was not merely harsh but brutal; several of his other apprentices had not survived it, and none had been able to meet his demands. Leia's and especially Luke's unprecedented capacity to do so only focused his attention more fully on them. He meant them to be Sith Lords after him, they knew, greater even than he was. The twins felt few aspirations in that direction; by twelve, they had only two desires left to them. They wanted to be free, to escape the grip of the Emperor, the Empire, and the Dark Side, and they wanted to see Palpatine die in agony. They saw no contradiction between these two driving purposes.
However, they certainly did not want to become what they loathed. They had no intention of turning into a pair of Palpatines, no matter what he did to them. Alone, their conscious resistance might very well have broken down, but they were always together, in mind and usually in person. They drew strength from one another even though they rarely suffered separately—Palpatine regarded them as one immensely powerful Force-user inconveniently split into two bodies. Most often, their mental talk was little more than screams vibrating across their minds: Luke—Leia—make it—please—not Leia—Luke, Luke!—Leia! But it was enough. Their unspoken defiance held.
Palpatine couldn't hear them. In the end, though, he guessed the truth, that they weren't a cosmic accident, but merely a pair of siblings interconnected in some way. Palpatine ordered them to fight one another. Not to the death, not yet, but he gently informed Luke that he would kill Leia if Luke did not fight her.
Luke attacked.
He was the stronger of the two, and the urgent need to control the power the Dark Side brought him had been drilled into his head almost from birth. Not from Palpatine, of course: from their father, who valued the Dark Side, yet knew better than to trust it. The duel ended with Leia's lightsaber clattering to the floor and Luke's hovering a few inches from her face. Had he been lost to the Dark Side, Leia would have died then—and Luke, though Palpatine never foresaw that, would have promptly followed her. Instead, he panted as he held the lightsaber at his sister's throat, her wide eyes staring unflinchingly into his; then he lowered his blade and stepped back.
When Palpatine ordered Leia to prove her worth, and defeat her brother—she was far more skilled in attack than defense—she refused. He didn't hold Luke over her head, but her own life.
Leia's lip curled. She tossed her lightsaber to the ground.
Luke saw Palpatine's eyes narrow, and lightning flashed past his eyes: Palpatine shooting lightning at Leia, Leia alone, and not only to teach her a lesson—
"Stay away from her!" he shouted, springing in front of his sister and focusing all his concentration on repelling the burst of lightning with his weapon. Palpatine shouted as his own lightning struck him. The lightning stopped, as did Palpatine's screams, but Luke didn't dare drop his lightsaber or break his attention. The Emperor gasped and then fell in a crumpled heap from his throne. Leia stepped out, summoning her lightsaber; Luke lowered his.
Did you—
"I don't think so," said Luke, bemused. They walked over to the Emperor; he was dead, his face still twisted in pain, one thin hand clutching his chest.
They looked at each other. Then, in perfect tandem, they threw their minds open. Sure enough, they could sense their father's presence nearby.
"Father?" they said, looking around in bewilderment. It was Leia who saw a shadow shifting by the servants' entrance to the throne room, just before their father stepped out. He looked strange: pale, and his eyes were as blue as Luke's used to be.
"Oh, there you are," said Luke. "Did you—"
Quiet; we cannot be too careful, Anakin told them both. I had not intended this to happen just yet. What happened? I could tell Leia was in danger—
He made us fight, Leia said. He told us it was the next step in our training.
Anakin's lips thinned. He walked over to stand by Palpatine's corpse, kneeling beside him and checking something with one gloved hand.
"The Emperor appears to have had a heart attack in the course of your training," he said. "Luke, send for a doctor to verify the cause of death."
Luke nodded and ran off. Leia looked at her father.
It needs to seem natural, doesn't it? Or you'll have to kill practically everyone on the way to the throne. That's why you didn't choke him, either.
"Poor Uncle Palpatine," she said aloud. "I suppose his heart was weak for a long time."
"Indeed," said Anakin.
Princess Leia, she thought. She liked the sound of it.
Twenty years later, the Rebellion overthrew the Empire. Emperor Skywalker died as he had lived, fighting on the front lines with his men. After a few years of distant and mismanaged government, the memory of his presence, courage, and firm rule would be invoked more fondly than anyone could have imagined, and his occasional atrocities quietly forgotten.
The Imperial Prince and Princess fled, under orders from their father. They were to bide their time, wait for the inevitable weaknesses in the infant Republic to arise, and then exploit them. Anakin himself could never have done it, but Palpatine had, and Luke and Leia were his protégés in ways that Anakin never had been.
For now, they concealed themselves—not at Bast, as their father had suggested (foolishly; anyone would expect it, and even they could not hold it forever), but their mother's and their old master's homeworld of Naboo. They didn't think of endangering their relatives there; the Naberries, too, would be obvious to anyone hunting them. Luke and Leia bought a waterspeeder and fled to the indifferent sea, making their way to an obscure, mostly abandoned property owned by their grandmother.
Luke drove the speeder, his shoulders straight and his hands resting lightly on the wheel. Leia, sprawled in the back, leaned on her hand and looked at him.
"It'll be all right," Luke said, with his usual reckless confidence. "We're together. No Sith Lords, no Empire, just us. There's nothing we can't do."
"That's true," said Leia. They had escaped it all, finally. She glanced down, into the smooth, cool water, and saw herself reflected back: strong nose, dark hair tangled around her shoulders, flat golden eyes. The Dark Side pulsed within her, within them both, as strong as ever.
It wasn't only in their blood, but their bones, their skin, their eyes, the threads of their lives. It would always be with them. Palpatine would always be with them. They didn't call themselves Sith Lords, but they lived as heirs to his empire, soaked in the Dark Side. She remembered screaming as lightning ripped through them after some minor failure, and remembered punishing subordinates with no more concern than Palpatine had shown towards them. She remembered the two of them looking dispassionately at Palpatine's corpse. She remembered those early holidays when they'd run, laughing, about Varykino, and even the later ones when their father took them to the races, just after their training began in earnest. They'd clapped and shouted like any other eight-year-olds.
It was a very long time ago.
Seven months ago, she'd discovered a spy onboard one of her starships, and ripped out his intestines with her mind. She hadn't felt anything but annoyance at the time. When she'd mentioned it to Luke, he'd said, "Well, he didn't have any more information, did he?" and shrugged.
She still didn't care. She didn't care about anything except herself and her brother. But she thought, now, that she should. Once, they would have. We were nice children, she thought dully.
They had been nice children. But they'd become monsters at Palpatine's hands — monsters like him, like their father, broken before them. Gone too far to bring anything to the galaxy but the same misery and torment that had consumed their lives.
"It'll be just like old times," Leia said, keeping her voice light. As quietly as she could, she unscrewed the lid to the fuel tank.
Luke laughed—happy, cheerful. His face was turned a little to the side, and she could see a tear slide down his cheekbone. The wind, perhaps. Or perhaps not.
Leia gathered the Dark Side close around her. I love you, Luke, she thought fiercely.
"Leia?"
She reached out a hand, just as Palpatine had taught her all those years ago, and shot a bolt of lightning out of her fingertip—right into the fuel tank.
The waterspeeder exploded.
More notes: In case there's any doubt, it's the bloodbending arc from LOK retold with Luke and Leia: Palpatine is Yakone, Anakin/Vader is the oblivious mother (with a touch of Yakone, himself), Luke is Noatak/Amon, and Leia is Tarrlok. Oh, and the Dark Side is bloodbending.
While I think fandom would lean more towards Leia as Amon and Luke as the (somewhat) gentler Tarrlok, I tend to quibble with the fanon that Leia is so much harsher and angrier and more like Anakin than Luke, and Luke as the older, more protective, and presumably more powerful sibling and Leia as the younger, more self-aware one seemed to match up better. I also think Leia's more likely to go through with a murder-suicide, and that it's much more probable that dark!Luke would be an idealistic, ruthless extremist than a cackling villain or alt!Vader.