Communication is key. Naruto and his sister could sit down and have an honest conversation about what's bothering him. They could clear up any misunderstandings that led to his hatred.
One possible reason could be a misunderstanding. Maybe some false information was spread about Kushina that made Naruto believe she had wronged him in some way. And for his sister, perhaps there was some sort of jealousy or miscommunication. For example, if his sister got more attention from their father or something similar.
Often, it portrays Dark Naruto as extremely bitter. He may be shown constantly thinking about Kushina in a negative light, with his every action towards her being full of malice. For example, he might plot revenge against her, even though she is dead in the original story.
Naruto might initially be in shock. He has always counted on Kushina's love, and this sudden abandonment would be a huge blow. He could become withdrawn and quiet, not understanding why his mother would do such a thing.
In a fanfiction like this, Fem Kyuubi's love for Naruto could be a deep, almost possessive kind of love. Since Naruto has always been different from others in how he treats the Kyuubi. As for hating Kushina, it could be that Fem Kyuubi blames Kushina for separating her from the world for so long. And this could lead to a lot of internal conflict within Naruto, who loves his mother but also has a bond with Fem Kyuubi.
The story could end with Naruto realizing his hatred was misdirected. After some big event or revelation, he discovers that his brother and sister actually care for him deeply. They all reconcile and become a closer - knit family.
One common plot could be that the sister has a different ideology. For instance, she might believe in a more radical approach to achieving peace in the ninja world compared to Naruto's more inclusive and forgiving way. This difference could lead to clashes and eventually Naruto's hatred. Another plot could be a power struggle. If the sister is extremely powerful and uses her power in a way Naruto doesn't approve of, like being cruel to weaker ninjas, it could make Naruto hate her.
Maybe she was forced to for some dark reason. Perhaps there was a threat to Naruto's life if she stayed, and she thought leaving was the only way to protect him.
In the fanfiction, it could be that Kushina is pressured by external forces. For example, there might be a powerful group or individual who forces her to abandon Naruto for his sister. This could be part of a larger political or power - play scheme. Also, it's possible that Kushina has a moment of extreme emotional confusion. She might see something in Naruto's sister that she once desired for herself when she was younger, and in a moment of weakness, she decides to focus on the sister instead of Naruto.
One possible reason could be jealousy. Maybe the sister is more favored by the villagers or has some special abilities that Naruto feels overshadow his own. This could lead to a sense of envy and ultimately hatred.