Perhaps in the fanfiction, Cersei's son discovers a hidden power within himself. He uses this power not for domination like his mother would, but to heal the broken kingdom. He might travel across the land, learning from the common people and using his new - found abilities to bring prosperity.
One possible plotline could be Cersei's son growing up to be a more benevolent ruler than his mother. He could see the destruction she has caused and try to make amends. Maybe he forms alliances with former enemies to bring peace to the Seven Kingdoms.
One possible plot could be that their son discovers the truth about his parents' tumultuous relationship. He might struggle with the knowledge that his mother had affairs and his father was not the ideal man he seemed. This could lead him on a journey of self - discovery, trying to figure out his place in the Seven Kingdoms.
In an interesting fanfiction plot, Cersei's son could be exiled from King's Landing. During his exile, he forms a band of outcasts. Together, they build a new community away from the power struggles of the capital. As he grows, he realizes that his mother's way of ruling is wrong. Eventually, he returns to King's Landing with his new - found wisdom and tries to overthrow his mother's tyrannical rule, not to take over but to establish a more democratic and fair system for the people of Westeros.
One possible storyline could be that Cersei's daughter rebels against her mother's tyrannical ways. She might see the destruction Cersei has caused and decides to take a different path, perhaps allying with the Starks to bring peace to Westeros.
He could influence events by being a voice of reason in Cersei's court. If he's intelligent and perceptive, he might be able to persuade his mother to make more diplomatic decisions rather than always resorting to force.
One possible plot could be the son growing up in the shadow of his mother's power-hungry ways. He might struggle with the expectations placed on him due to his family name. For example, he could be groomed to be a political pawn but secretly desires a more peaceful life away from the power struggles of King's Landing.
Perhaps Cersei's son, having grown up seeing the chaos his mother caused, could bring about a new form of governance. Instead of the feudal system that was prevalent, he could introduce a more democratic - like system where the voices of the lords and the common folk are heard. This would be a huge change from the power - hungry struggles that were characteristic of the Game of Thrones world.
The son's character might develop as he uncovers family secrets. Knowing about his mother's true nature and his father's misdeeds could make him question his own identity. He could start as a naive young man, but as he digs deeper, he becomes more cynical. But instead of being consumed by it, he decides to break the cycle of corruption and lies that his family has been part of. He could start to develop his own moral code, different from the cut - throat ways of his parents.
Some of the more independent lords or ladies in Westeros could be allies. For instance, Lady Brienne of Tarth. She is a paragon of honor and if the bastard displays honorable intentions, she could offer her sword and protection. Also, the wildlings might see the bastard as a way to gain some influence in the south. If the bastard offers them something in return, like a place to settle or resources, they could form an alliance.
There's also a possibility of her allying with some of the more neutral houses. Houses that were tired of the constant fighting between the big players. Her daughter could offer them stability and protection in exchange for their loyalty. She could present herself as a new hope for a more peaceful Westeros, which might attract these houses to her side.