Annabeth is known for her intelligence and strategic thinking. She is a strong and independent character. Percy, on the other hand, is brave and has a strong connection to the water due to his father being Poseidon. In the fanfic, when Annabeth sits in Percy's lap, it might be a way to show their unique relationship which has developed over the course of their many shared experiences in the Percy Jackson universe.
Percy might be a bit flustered and embarrassed. He's protective of his relationship with Annabeth, so having Magnus walk in might make him feel like their privacy has been invaded. He could quickly try to shield Annabeth or just look really shocked.
Their shared experiences play a big role. They've been through so much together, like countless battles and adventures. Percy has seen Annabeth in tough situations and he knows how strong she is, but also how vulnerable. So he feels the need to protect her. For instance, they might have had a close call in a previous adventure where Annabeth was nearly killed, and that memory makes Percy extra vigilant.
Their relationship is likely to be complex. They are friends and comrades who have fought side by side many times. So, there's a strong bond of loyalty between them.
Percy might develop more of a steely determination. In Tartarus, he has to face extreme danger, which could make him even more resolute in protecting Annabeth and getting out. Annabeth, on the other hand, could become more resourceful. She'd have to use her wits in this strange and deadly place.
They can develop their relationship by having deep conversations. For example, sharing their fears and dreams about their future together. Maybe Percy tells Annabeth about his insecurities of not being a good enough husband sometimes, and Annabeth reassures him.
They would likely raise them with a strong sense of honor and courage. Percy would teach them about the power of the sea and how to use it for good. Annabeth would instill in them a love for knowledge and strategy. They would also train their twins in combat skills to protect themselves in the dangerous world of demigods.
It could also be due to some sort of magic or mind - control. A powerful enemy might have cast a spell on Annabeth, forcing her to turn against Percy. In this case, it's not really her own will but the result of external manipulation.
The relationship will likely grow stronger. They'll have to rely on each other more for daily tasks and support. For example, if Percy has a bad day at work or school, Annabeth will be there to comfort him right away, and vice versa. However, it could also be a bit strained at times. There might be moments when they feel suffocated by each other's presence, but they'll have to work through those feelings to keep their relationship healthy.