AU: Anakin turns on Palpatine when he reveals himself as a Sith so Palpatine tells him that Anakin will be the cause of his wife's death. Anakin, because he's in a terrible state, feels this is true and so after he kills the Chancellor he runs away to Tatooine because he's convinced he should suffer.
He becomes Beru Whitesun's problem, when she finds him crying at his mothers grave one morning.
Meanwhile - by the time Obi-Wan comes back from Utapau the Chancellor is dead, Padme is in labor and Anakin is in the wind.
Both the Jedi and the Senate still have to finish and clean up the war( since the Separatist leadership is still alive) deal with the Clones rights and roles post-war, and basically try and put the huge mess of the Republic back together.
Plus Obi-Wan has to help Padme with her suspiciously powerful Force-Sensative twins while the Senator refuses to stop trying to work while in a state of Force Exhaustion from giving birth to said babies as a non-Force-Sensitive (because why not?)
Beru Whitesun, meanwhile, has a highly skilled and very miserable Jedi Knight on her hands, and she decides that she may as well put him to Work.
Anakin had a dream once, that he came back and freed all the slaves.
And he tends to solve a lot of his problems with his lightsaber. So. Anakin goes on a very swift and violent rampage and the slaves overthrow Tatooine and make a treaty with the Tuskens over their ancestral lands and in a way this is how Anakin makes reparations for the slaughter of that Tusken village. Now, Anakin is not suited to lead a government, so his job after - when he's not moping on Owen and Beru's farm, is fending off attempts by the Hutts to retaliate or reclaim Tatooine.
Anakin learns things about the sheer span of his power, fighting alone, not all of them good. He learns things about himself too, kneeling at his mothers grave. It becomes a sort of meditation, sitting there in the sands, confessing everything to Shmi Skywalker's ghost.
Obi-Wan, deputy Head of the Order, semi-co-parent to Luke and Leia Nabberrie, eventually tracks reports of conflicts near Hutt Space to his Padawan and finds Anakin on Tatooine, alive if not entirely well.
It takes months of trips back and forth to Tatooine to convince Anakin to at least come to the Temple.
Anakin refuses to meet Padme, still terrified and convinced that he will be the cause of her death.
He has no choice about meeting the Twins, who heard Obi-Wan found their father and snuck across Coruscant to see him.
Luke is very shy, actually meeting him. Leia beats him with a couch pillow for making her mother sad.
Anakin just cries, which makes Leia very awkward and Luke tries to console him.
Anakin feels too far from what a jedi should be to stay, but Obi-Wan convinces him to at least call Padme - which Anakin does, once he's half the galaxy away again.
They have to get to know each other again, and this is different than the first time, harder and slower and so much more real than their frantic, desperate feelings at the start of the war.
Ahsoka eventually returns to the Order and rises to Knighthood. She spends most of her career thereafter specializing in rescue operations and finds a little bit of passion for teaching classes at the temple.
By the time the Twins are ten, Leia's favorite Jedi is Master Windu, who knows very little peace because of this. Luke is definitely his mothers son, and while he finds a great deal of peace in the temple when they visit Uncle Obi-Wan, and he's good at meditation, he spends most of his time in Senator Amidala's office, and shadowing her in diplomacy.
They work a lot with Senator Fox (who knows over half the Senates dirty secrets, not that anyone dare accuse him of blackmail) on Clone Rights and Resettlement, and Luke's unofficial occupation is to be very cute and innocent and hold Senator Fox's hand when it seems like there might be a murder to prevent.
It's a devastatingly effective tactic.
Tatooine is a free, established world, and there isn't much trouble there now - especially not with Trooper Town just beyond Mos Espa, ready and willing to defend their little bit of peace.
Tatooine needs a Representative, and Beru makes Anakin do it. He's still not entirely sure how, by the time he's landing on Coruscant and there is Padme, welcoming "Ambassador Skywalker" and there is a little of that fear, still, but he also feels so, so foolish for ever running away from her.
Anyhow, Leia becomes a Jedi (apprenticed to Master Windu) and spends a good deal of her adolescence and early adulthood trying to beat the snot out of her father with her lightsaber. By the time she's good enough to actually win, the desire has largely gone away.
Luke succeeds his mother as Senator Amidala of Naboo, with special permission from the current queen to borrow his mothers royal title.
Anakin and Padme re-wed, this time with all their friends in attendance, this time knowing really what love is, and what it takes to make something of it.
Anakin eventually follows his wife into Retirement, though in truth neither of them really settle. They're barely middle aged and there has always been a bit of fire burning in both of them.
It's not ever trule easy, life after war, but it is good.
Obi-Wan visits their home in the Lake Country at least once a year. He trains a new padawan every decade and there isn't a single one of them that Anakin didn't save from a spot of trouble at least once, in spite of insisting he didn't like any of them for one reason or another. There also isn't a single one of them that doesn't inform him that Obi-Wan always talks about him, and there isn't a single one of them Anakin doesn't provide with "secret" advice on how to handle being Obi-Wan's padawan.