Rin and Yukio are faternal twins born to Yuri Egin, as the result of being impregnated by Satan. In this, though, both twins are female rather than male.
With some difficulty, Shirou raises the girls in the abbey to the best of his ability. But they both grow on him quickly and he strives to be the best father he can be.
When Rin is six, she gets in to a nasty fight at school, her hidden demon traits nearly breaking through and causing her to injure several students and a teacher. Fearing retribution from Shirou, she runs away and stumbles across a group of unruly teenagers smoking, drinking and gambling. They harassed her, pushing her around while they offered to "play" with her. Panicked and still running on the energy from the previous fight, she lashed out, and woke her flames for the first time.
Thinking it was some kind of cool magic trick, she decided to keep it under wraps and tried to bring it back out again, without much success. About a month after the first time, she was able to produce a tiny bit of flames again, but at the cost of utter exhaustion. So she kept working at it, again and again, eventually getting more and more but to the point of overtaxing herself until she passed out at school.
She backed off from practicing, letting Shirou believe she had simply come down with an illness, until at last she was able to do it well enough that she could finally show Shirou and Yuki both. Shirou was shocked, and upset that her flames had woken so early, but he also resolved to give Rin proper training because of it. Even if she could never become an exorcist in the certified sense, he wasn't about to leave her to her own devices.
He gave her a pendant that acted in a similar capacity to the scabbard of the Kurikara - the ancient demon slaying sword that had originally sealed Rin's power - by giving her an active seal that would only let her flames appear in an absolute emergency. He promised she would have the wards on it lifted bit by bit until she was completely capable of controlling them on her own. With this they began a regiment in a sealed room that hid her powers from the rest of the demonic world that involved martial arts katas and focus training with candles and other flammable materials. It was around this time that Rin took to the kitchen as another outlet, learning to cook by trial and error so that they could live off more than just barely passable curry and other plain foods.
Shortly after, Yuki attempted and succeeded in unlocking her own flames. Unlike Rin, however, she already had a great deal of control over them. Because of this she was spared the need for the pendant, though she decided on her own that she wanted to train with her sister if only to give her a sense of not being alone in it. She also started her own proper exorcist training, picking up and very quickly learning fire arms as if they were an extension of herself.
Eventually, Shirou began taking her out on "moonlight missions" - not necessarily missions that took place at night but ones that were small enough that the Order wouldn't likely catch wind of what they were doing. She got hurt the first time out, causing Shirou to realize that she needed more than just her fists to carry her through. With that in mind he employed an old student of his - Shura Kirigakure. Shura begrudgingly agreed to teach Rin the sword.
Shirou didn't want to give her the Kurikara quite yet though, for fear of what completely unlocking Rin's powers would bring, but instead had a special sword crafted for her when she had become skilled enough with a training blade. Shura created a space of holding for her on a bracelet, and the weapon was concealed with in it, ready to be pulled at a moment's notice. Her training and the occasional missions with Shirou continued while Yuki started to advance swiftly through her own exorcist training, but all the while Rin was left with a hollow feeling that something wasn't quite right.
That was because all this time, Shirou had still been keeping an even bigger secret from Rin - namely who her real father was. Rin had, over time, come to understand that she was not fully human. Humans didn't burst in to flames, not even well trained exorcists. Humans couldn't hear other demons. Humans didn't have their teeth and ears grow and become pointed as they grew up. But as far as she understood she was likely the result of some poor human woman and a higher level demon that knocked her up for the hell of it.
In school she got in to fights constantly, especially with the resident bullies. She hated seeing the injustice being done to so many younger, weaker students and always tried to stop it, but in the end it always left the bullied more afraid of her than anything, and the bullies themselves even more pissed off.
Eventually one of the fights ended with her ducking out from the class room and running away as she had when she was little, hiding in the park until a boy from her class found her. Maka Albarn had been watching her for a while, finding her interesting and not nearly as scary as everyone perceived her to be. In fact he rather admired her for being willing to stand up to the bullies at the cost of her own integrity. When Rin admitted she didn't want to go home right away, he offered to let her go back to his place for the night, just to cool her head. Rin agreed, but what should have been a peaceful night was broken by the revelation that the quiet, bookish boy had been dealing with his own demon for years, quite literally in fact. A higher level demon fed off his negative emotions, and was angered by the cheerfulness Rin had brought with her. Rin dispatched the demon with some difficulty thanks to it's attachment to Maka, but soon enough he was freed and Rin's position as a sort-of-exorcist was revealed.
Not long after Rin went through the very painful process of having her tail rather suddenly grow in. She was out for a week, but upon returning she found that Maka wasn't at all bothered by her or what she was, and didn't mind being friends even if all the other students made noise about it.
As much as she disliked school, she suffered through it for Yuki's sake, and to stay near the one friend she had managed to make during that time. She knew there wasn't much she could do aside from get low level work outside of school if she quit, and being a secret exorcist wasn't going to pay bills, which was something Yuki worried about profusely. She wanted the best for her older sister and begged her constantly to at least try to stick it out, even after she was accepted to the prestigious True Cross Academy on a scholarship. It was even harder to stay in school after that, especially since she was alone at a much lower class school, but she continued on anyway. Being around Maka made it easier.
While heading to an interview she was confronted by another girl she often had confrontations with at school - Rei Shiratori. Rei had a history of being cruel to people and animals alike, and she had been the one that Rin had stopped from harassing the younger students some weeks before. She was back for round two with her cronies, and that's when everything went strange. Rei became possessed by one of the demon kings - Astaroth, the King of Rot, who throughout their fight dropped hints and clues that Rin was not mere the daughter of a demon.
Eventually Shirou managed to arrive and banish the demon from the girl, but Rin was left with more questions than answers. She demanded to know what was going on, and Shirou admitted the truth - her true father was none other than Satan himself.
Rin was furious to find such a thing out, and while she returned home and stewed about it long enough to be rightfully pissed at Shirou, she was still willing to listen to him because really... Shirou was the only father she ever knew. But the trust had been broken, and even though she decided in the end to forgive him because he did have his reasons, that didn't stop her from passive aggressively tormenting him for some time after.
Unfortunately the incident trickled through the right pipelines and Mephisto showed up some time later, demanding to know with that usual smile of his why Shirou had never told him that Rin's flames had awoken so long ago. Shirou did a good job of dancing around the answer, but their talk did eventually turn to the subject of Rin becoming an exorcist and attending the cram school at the prestigious True Cross Academy along with her sister.
Shirou was adamantly against it, too afraid of what would happen if Rin's origins were revealed, but Mephisto put up a good enough argument for it - what better way to protect Satan's daughter than right under the noses of the very people set out to destroy him? Could Shirou really protect her forever on his own, knowing that sooner or later she would have to make her way in the real world without him at her back every step of the way?
Eventually he agreed, with much reluctance, and informed Rin that she would be transferring. The only thing that made her upset was leaving Maka behind, but those worries were quickly put to rest when Maka revealed that he, too, would be going to True Cross. Not only that, he was enrolling in the cram school.
So Rin began cram school with her new friend and her sister at her side, with no idea what the future would hold for her as the daughter of Satan...