This story includes the TV shows Buffy, the Vampire Slayer and Gilmore Girls, the second being only a minor cross, and the book series Twilight. Later on (I'm not sure when exactly), I'll be bringing in a fourth cross, which is a surprise. BtVS belongs to Joss Whedon, GG goes to Amy Sherman-Pallino (sorry if I misspelled that), Twilight belongs to Stephanie Meyer, and the last one is, of course, a surprise.
This is an explanation of events that happened prior to Infinity. As I do not feel like they warrant a whole story, I will be what happened so you can better understand the story itself.
Shortly after Willow returned to Sunnydale after her stay in Devon, the Summers sisters were told of fatal events concerning their family in Connecticut. Their Aunt Lorelai, their mother's younger sister, had died in a car accident and her daughter, Rory, was comatose in the hospital. According to her will, Lorelai's teenage daughter was to be placed in the care of her older sister, except Joyce had died a couple years previous so Rory was placed in Buffy's custody until her eighteenth birthday.
The sisters flew out to attend Lorelai's funeral and collect Rory, who was in desperate need of a blood transfusion. Dawn, who happens to be the same blood type as her cousin, donated almost half of her own blood supply. Rory was discharged in time for the funeral, after which they returned to Sunnydale.
Upon arrival in the small town, Buffy laid down the most important rules – do not go out after nightfall, do not give verbal invitations into the house, and under no circumstance eat her low-fat yogurts. However, the teenager didn't take her seriously and went our for a walk that night without telling anyone that she was leaving.
She walked through the park, where a vampire jumped her. Luckily, Buffy was passing through the same park and ran across them. After staking the vampire, she thoroughly chewed Rory out for breaking the rules. After learning about the supernatural, Rory and Dawn grew close, being the only teenagers in the group. They bonded over research, the only contribution they were able to make to the Scoobies.
After the Collapse, the Scoobies drove to LA, where they recuperated in Angel's hotel, before heading to England to rebuild the Council, which they renamed Sineya's Council after the original Slayer. While in LA, the two groups discussed forming bonds between the Council and LA's branch of Wolfram&Hart, which the AI Crew had been offered control of. They agreed and took Connor with them so he could get the help he needed from the witches in Devon. Rory and Dawn were shoved into private school to repeat their sophomore year of high school since they both managed to flunk in Sunnydale.
The story picks up about a year after the Collapse so the two teenagers are now 17 and Buffy is 24 and working on her degree in counseling psychology.