I thought about this AU and I realized I don't think this can be a complete AU swap considering her state of mind during the events of Revenge of the Sith and who she is. Here’s what I think an AU of this would look like, I hope it’s okay it’s not exactly what the prompt requested:
At the start of RoTS it would've been a few months (year?) since Ahsoka walked away from the Jedi Order and Ahsoka was disillusioned but she still helped the Jedi when she could.
Namely when she helped organize a resistance against Darth Maul (guy has more lives than a cat) in Mandalore. Ahsoka went toe to toe against Maul and if Order 66 hadn't been activated, she would have captured him.
So if we diverge from the moment Rex (Anakin's loyal right-hand man in the 501st) faked both his and Ahsoka's death the AU can start before Ahsoka goes into self-imposed exile, somehow Ahsoka managed to intercept a message from Obi-Wan about Padme's condition, and the rendezvous point at Polis Massa.
Relieved someone she knew was still alive, grief-stricken, and looking for guidance Ahsoka made her way to Polis Massa just in time to see the twins born and Padme die.
Obi-Wan is beyond relieved that Ahsoka survived and invites her to the meeting room with Yoda and Bail. Ahsoka is horrified at Yoda's plan to separate the twins but Yoda overrode her concerns stating the needs of the many outweigh everything.
Frustrated, Ahsoka volunteered to take Leia with her before Bail could suggest he and Breha could adopt Leia.
After a few second's deliberation, Yoda agreed and Obi-Wan was still too shell-shocked to say anything but a token resistance. They all agree to go their separate ways.
Except Ahsoka realizes she bit more of than she could chew because aside from creche duty Ahsoka didn't know anything about raising a child, much less taking care of a baby.
It's a huge learning curve.
This was when I debated if Ahsoka and Leia could lay low in Tattooine but the more I thought of Ahsoka and Leia getting stuck in Tattooine I realized it would be a slow torturous death for Ahsoka. Ahsoka is a being of movement and shackling her to a planet would kill her. Even as an adult, she never stayed in one planet for long.
Obi-wan Kenobi can lay low on a planet for decades due to a combination of his adherence to the Jedi teachings, guilt and because of the training Yoda asked him to do.
Also, there would be no way in hell Ahsoka would let Owen drive her out of Leia's life. Another reason why she can’t really stay in Tattooine was because certain pirates of Ahsoka's acquaintance might hang around Mos Eisley and identify her. So just like in the Ahsoka novel Ahsoka would decide to settle down in outer rim planets taking on the nondescript identity of Asha.
Ahsoka decided to keep Leia's name.
The events in the Ahsoka novel went down almost similarly except that there's an added complication of Leia, fortunately Ahsoka seem to instinctively draw people in who could help her and the Faardi clan were more than accommodating in both helping Ahsoka to live a nondescript life as a lowly (but talented) mechanic in Thabeska but also help guide Ahsoka raise a baby.
This makes Ahsoka's abandonment of Hedala that much harder but she makes sure when she returned to Thabeska, she would help Hedala control some of her Force powers so she won't accidentally draw any inquisitors to her.
This also helped Ahsoka decide how to handle Leia's Force powers when they start manifesting.
This leads to Ahsoka's time in Raada and how she's even more cautious when the Empire arrives in the Farming Moon but tldr Ahsoka managed to contact Bail and free the people of Raada and get them in contact with the budding rebellion. The Raada people are relocated to a Rebel friendly peaceful planet while helping the rebellion with their food production.
This meant stability for Leia, Ahsoka could safely take care of Leia among a group of people she trusted. A village helps raise Leia
(In this headcanon Ahsoka lived with Kaeden, a woman she met in Raada. In the Ahsoka novel Ahsoka rescued Kaeden from an imperial jail and in rescuing Kaeden razed an Imperial facility. After a lot of false starts and Ahsoka trying to get over a lot of her Jedi hang-ups Kaeden and Ahsoka are a couple, so Leia also grew up with a family.)
Learning from what happened with Hedala Ahsoka started teaching Leia about the Force: how to use it and block it, and how to fight. She would also tell Leia how the Order lost their way, and in a lot of ways the Jedi were also the architects of their own destruction. She would tell Leia all about her parents, and her brother. She wouldn't see why there would be a reason to keep those details from Leia.
(Yoda didn't tell Ahsoka about Vader = Anakin.)
As Leia grew-up Ahsoka became more and more active in the rebellion, establishing the intelligence unit and creating lines of communications between different contacts. The moment Leia turns 16 years old, Leia begins to make noises about joining the rebellion.
Kaeden stays away from this argument between Ahsoka and Leia, Ahsoka wanted to keep Leia safe but Leia is persistent and even points out how unfair it was since Ahsoka fought in a war when she was younger than Leia ("that doesn't make it right, Leia.")
Kaeden does intervene when things become heated between Leia and Ahsoka, eventually Ahsoka caves (Ahsoka would think back to all her insolent and snippy moments as a teen and she would have a strong urge to apologize to everyone who knew her back then) and allows Leia to join as a messenger.
Leia went by Leia Tano growing-up. Sometimes Leia Nebarrie in her messenger duties.
Ahsoka would realize Leia would need more education and arranged for Leia to stay with Bail. As Bail's ward Leia was in a good position to coordinate with Bail and Breha's government without risking Bail's dual role as senator and founding member of the Rebel Alliance.
Then the events of Star Wars Rebels season 2 happen. Ahsoka lived a very compartmentalized life, Ahsoka never mentioned Leia to the Ghost crew, not even with Rex and then Ahsoka finds out about Vader and, then later who Vader was. Furious, Ahsoka tracked down Obi-Wan and shouts at him before she goes to Malachor.
She wanted to help Anakin but not just that, she wanted to reunite Anakin with Leia but not when he was still Vader.
She fights Vader harder than ever.
Both Leia and Kaeden wait for Ahsoka to return but months pass by and word gets to them that Ahsoka could have died at the hands of Vader. Kaeden is grief stricken but Leia, Leia is angry, she moves to Alderaan permanently and takes the Organa name.
(She still visits Kaeden when time permits).
The events of Rogue One happen and it happens almost exactly the same way as they smash cut right into A New Hope with Leia lying to Vader's face about the plans while sending off her message to Obi-Wan.
The message would be something like: "Master Kenobi, I am Leia Organa and I was ordered to bring you back to Alderaan but my ship was attacked. I've placed information vital to the survival of the Rebellion in this R2 unit. You must see this droid safely delivered to Alderaan. Help me, Obi-Wan Kenobi. You're my only hope."
The other part I'd make in A New Hope is that Leia would be part of the squadron that takes down the Death Star. Luke can have the kill shot but Leia would be the one covering his six.
A New Hope would be a turbulent time for Leia not only because of Alderaan's destruction but because she was happy she finally gets to meet her brother only to realize Obi-Wan never told Luke about her or their parents.
In this AU Leia’s made more of a headway in her study of the Force so she helps Luke learn about the Force. Leia is also a bit angry at Obi-wan for not preparing Luke.
They both become ‘a Jedi like their father’ but Leia adds on her responsibilities in the Rebellion just like in the original canon due to her experience and Ahsoka's teachings.
Leia, btw, would have the satisfaction of yelling at Yoda.