I'm not sure if this has been explored before, but the Twilight series seems very reminiscent to Natalie Babbit's
Tuck Everlasting and I think it could be the other book that correlates with Breaking Dawn.
For those who are not familiar here is Tuck Everlasting in a nutshell:
Tuck Everlasting is a novel about a a young girl, Winnie, who acquaints herself with the Tuck family. The members of this family have become immortal from drinking from an enchanted spring. Winnie, who falls in love with the youngest son Jessie, has to make the decision whether or not to drink from the spring and become part of the Tuck family forever. In the end, she decides to leave the family in order to enjoy a normal human life.
Tuck Everlasting visits the concept of living forever, and why it may not be as beneficial as it appears at first glance.
Could it be this is the other story Stephanie Meyer was referring to?
I can see Bella's moral decision(about whether to go through with becoming a vampire) reflected in Winnie's complications in drinking from the spring. Even though Bella's decision has been revisited many times throughout the series, I still think there is a possibility she may re-think becoming a vampire.
Though I love Bella and Edward and sincerely want her to join the Cullens, I find a startling connection between these two love stories.
If this story was played out through Breaking Dawn, Bella would rethink her decision about joining the Cullen family and live the rest of her life as a human.
EDIT: And as irrevocably_intoxicating pointed out, in the end Edward would visit Bella's grave.
I hate this connection, but I feel like I should share it.
By the way, I just read the Twilight series a couple of weeks ago and completely fell in love with it! I enjoy your podcast and I hope you keep up the good work!
Thanks!