They might become more protective. Since they are dreaming of having a daughter, they would start to think about all the potential dangers she could face. Their relationship could grow deeper as they bond over their shared hopes and fears for their future child.
She could be a strong and intelligent girl, just like her parents. Maybe she has Percy's sea - green eyes and Annabeth's blonde hair. She might inherit Percy's ability to control water to some extent and Annabeth's strategic thinking.
Her adventures could start right in her own backyard, so to speak. She might discover a hidden entrance to an ancient labyrinth in her neighborhood. As she explores it, she has to use her wits and any powers she has. Later, she could be drawn into a larger adventure where she has to stop an evil force from awakening an ancient and powerful Titan. She would travel across the country, or even across different continents in the demigod world, encountering various mythical beings. Some might be friendly and offer her help, while others would try to stop her at all costs. And through all these adventures, she would grow in strength and wisdom, just like her parents did before her.
Maybe there would be some initial tension between Percy and Annabeth's daughter. She could be rebellious and not want Percy interfering in her life at first. But as time goes on, they could form a strong bond. They might go on a quest together, where Percy has to save her from a dangerous foe, and that's when their relationship really starts to grow and develop into a more trusting and loving one.
One possible plot could be that in their dreams, they see their daughter growing up in a world where the threats they faced are no more. She is strong and confident, trained in the ways of the demigods. They dream of her making friends easily at Camp Half - Blood and having a special bond with the nature spirits there.
It could be an old enemy of Percy and Annabeth. Maybe a monster that they thought they had defeated long ago but has come back for revenge. This time, it might target Annabeth's daughter to get back at them.
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.
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.