For Bella, a nightmare could involve her not being able to control her vampire instincts and accidentally harming someone she loves, like her father or one of her human friends. This would be a huge source of distress for her. Carlisle might have a nightmare where the Cullen family is ostracized by the vampire community for some reason, like breaking an important vampire law. He would be devastated as he has worked so hard to build a harmonious existence for his family within the vampire world.
One idea could be Carlisle having to protect Bella from a new vampire threat that is specifically targeting her for her unique connection to the Cullens. Maybe a group of nomadic vampires who are jealous of the Cullens' lifestyle.
The Cullen family members are important characters too. Edward, for example, might have an interesting dynamic with Bella in this fanfiction. He could be either protective or jealous of Carlisle's special relationship with her.
Many fans would likely be divided. There would be those who are open to new interpretations and might find it an interesting take on the characters. However, a large portion would probably be against it as it goes against the established love story between Bella and Edward. They might feel that it changes the essence of the characters as they were presented in the original books.
A possible plot could be that there is a threat to the vampire community that only Bella and Carlisle, with their combined skills and knowledge, can solve. As they work together, they start to see each other in a different light. Carlisle might see Bella not just as a young vampire but as a strong and intelligent equal, and Bella could gain a deeper respect for Carlisle's wisdom and experience. During this time, their relationship could evolve in unexpected ways, like a deeper friendship that is on the verge of something more, but they are hesitant due to the age gap and their different roles in the vampire family.
Bella's nightmares can also show her struggle with her new vampire identity. If she has a nightmare about not being able to control her thirst, it ties into her character's journey of self - discovery as a vampire. She was always a bit of an outsider as a human, and now as a vampire, she has new challenges to face. Carlisle's nightmares about his past sins are very much in line with his character. He is a morally upright vampire, constantly trying to atone for his past actions. These nightmares are a reminder of the internal conflict he has between his past and his present self, and how he is always striving to be better.
Maybe Carlisle and Bella could bond over their shared experiences of being different from the norm. Carlisle is a 'vegetarian' vampire, and Bella is a human who is in love with a vampire. They could have deep conversations about how they both struggle to fit in with their respective worlds and find solace in each other's understanding. This would add a new layer to their relationship and make it more unique.
One interesting plotline could be Carlisle training Edward and Bella to better control their vampire powers. This would involve a lot of interaction between the three characters, with Carlisle using his experience to guide them. Another could be them facing a new vampire threat together, where Carlisle's leadership, Edward's abilities, and Bella's unique perspective as a former human come into play.
Often, it starts with an unexpected encounter or a moment of realization. Maybe Carlisle sees Bella in a new light, not just as Edward's girlfriend but as an individual with her own charm. Then, there are small gestures of kindness and understanding between them that gradually build up the relationship.
There could be Edward. Even though the focus is on Carlisle and Bella, Edward's presence might still be felt as he was an important part of Bella's life before. His reactions to Carlisle and Bella's relationship could add some drama.