I'm not that familiar with her, but she must be the central figure in this story. Maybe she was someone who went through an extraordinary event related to judgment.
They could go on a quest to find a magical artifact that has the power to keep both the demigod world and the Twilight world in balance. Percy's skills in combat and his knowledge of mythology would be useful, while Bella's ability to understand the motives of vampires and werewolves could help them avoid certain dangers.
Alice is often quite popular. She has the ability to see the future, which can add a lot of interesting twists to the story. For example, she might see a danger coming towards Bella and Edward and try to prevent it. Her quirky personality also makes her a favorite among fans.
In this fanfiction, their relationship could be tested in new ways. For example, they might have disagreements on how to raise the child, or how to balance their need for survival with the needs of the pregnancy. This could lead to some tension but also deeper understanding between them.