A third storyline could be that she gets transported to a different time or realm. There, she has to rely on her wits and powers to survive and find her way back home. Along the way, she meets new characters who help her understand more about her parents' pasts and also about her own potential. This could involve her having to solve ancient riddles and battle unknown foes with only the skills she has learned from Percy and Annabeth.
One possible storyline could be that their daughter inherits both of their special abilities. For example, she might have Percy's skill with water and Annabeth's strategic mind. She could go on adventures in the same world as her parents, facing new monsters and challenges. Maybe she discovers a long - lost secret related to the gods that her parents were unaware of.
Another storyline could be about her trying to live up to her parents' legacy. She could feel a great pressure because everyone expects her to be as great as Percy and Annabeth. She might struggle at first but then find her own way to shine, perhaps by using her unique combination of abilities in a different way than her parents did. She could make new friends and form a team of her own to face the threats to the demigod world.