The development might also involve the kids growing up and trying to find their place. They would be different from other demigods, so they would have to create their own identity. They could form alliances with other outcasts in the godly world and try to change the way things are done.
It could start with the unexpected union of Percy and Artemis. Maybe some sort of magic or a unique prophecy brought them together. Then, as they discover Artemis is pregnant, they would face a lot of shock and disbelief from the other gods.
At first, Percy might be confused about his connection to Artemis. But as time goes on, he starts to understand her values more. He may learn to respect her love for nature and the hunt. Their relationship could develop into a strong bond of mutual trust, where Percy becomes one of Artemis's most trusted allies in her various battles or quests.
In the beginning, Artemis would be the strict but loving adoptive mother. She'd teach Percy everything she knew. Percy would look up to her with admiration. But as he gets older, he may want to explore his own identity more, especially his connection to Poseidon. This could cause some strain in their relationship. However, through various adventures and challenges, they would come to understand and respect each other more, and their relationship would become more of an equal partnership in the end.
Percy may develop by becoming more aware of the divine female perspective. Since Artemis is a goddess, her presence can make Percy think differently. For Artemis, she might develop a softer side. Usually very stoic, interacting with Percy could make her more empathetic.
They might inherit Percy's courage and Artemis' connection to nature and the hunt. Maybe they'd have the ability to control water like Percy and also be excellent archers like Artemis. Their personalities could be a blend of Percy's fun - loving and loyal nature and Artemis' independence and fierceness.
Often, it starts with a small incident that sparks the hatred. For example, Percy might save a person or creature that Artemis was hunting, thinking he was doing the right thing, but from Artemis's perspective, he's interfering. Then, the relationship deteriorates as more misunderstandings pile up. Artemis might start to actively oppose Percy in his quests, using her own powers and influence against him.
Percy would likely develop a deeper sense of compassion and understanding. He's used to dealing with powerful beings, but a disabled Artemis would show him a different side of the gods. Artemis, on the other hand, would have to learn to rely on others, which is a big change for her. She might become more humble and see the value in teamwork. For example, Percy could teach her some of his survival skills, and she could in turn share her knowledge of the hunt.
One way it could work in a friends fanfic is if there's a parallel universe or alternate reality where the rules of the gods are different. In this realm, Percy and Artemis might be brought together under special circumstances. Their kids could then be a symbol of a new era or a new hope for the world they inhabit, and their friends could play important roles in protecting or raising these children.
Well, in a fanfic, their kids could have a very complex relationship with the world of the gods. They might be seen as something of an anomaly because Percy is a demigod and Artemis is a virgin goddess. So the kids would have to deal with a lot of prejudice and misunderstanding from other gods and demigods.
In the fanfiction, their relationship development could be complex. Since they are sharing a bed, there is a forced closeness. Percy might accidentally cross some of Artemis's boundaries at first, which would cause friction. But through talking it out and getting to know each other better, they could start to respect each other's boundaries more. As time passes, they might find common ground in their love for nature (in Percy's case, his connection to the sea which is also part of nature). This could lead to a slow but steady growth of a relationship that is based on mutual understanding and respect.
Their relationship might develop through facing external threats. For instance, if there are enemies that target them because of their forced union. They would have to rely on each other's skills. Percy's ability to control water and his combat skills, along with Artemis's archery and connection to the wild, could be used to fend off these threats. As they fight side by side, they start to see each other in a new light and develop a bond.