Perhaps a rival king. If there are two kingdoms, the rival king may see the daughter as a means to gain power over the king's kingdom. He could try to kidnap her or use her in some political maneuver.
I don't know who specifically told this 'king killed his daughter story'. It could have been an ancient storyteller in a long - lost tribe, or an author writing a fictional piece.
The main plot might be about the king protecting his daughter. Maybe there are threats to the kingdom and the king has to keep his daughter safe from all kinds of danger.
The mother's new partner. He doesn't want the forgotten daughter to be part of the family as he fears she will disrupt the new family dynamic he has been trying to build. He might use various means to keep her away from the family.
A group of rogue demigods could be the main antagonists. They might be jealous of the attention the daughter gets because of her parents. So, they plot to make her life difficult and try to drive a wedge between her and the other demigods.
A powerful demon who wants to take over Crowley's territory might target his daughter. By getting rid of her, they believe they can weaken Crowley and then take what he has. This demon could be very cunning and use all sorts of tricks to get to her.
Maybe an organization that wants to use her unique abilities. If she has inherited some special power from Kakashi or has her own distinct skills, an evil organization could try to capture her and force her to work for them. They would be the main obstacle she has to face in the story.
A new supervillain who has emerged and wants to make a name for themselves. They think that kidnapping Tony Stark's daughter will draw him out and give them the chance to prove they are a force to be reckoned with. They might also be after Tony's wealth and resources which they can access through his daughter.
It could be a powerful vampire from a different coven. Maybe one who sees the daughter of war as a threat to their power or territory in the Twilight world.
King Midas' wish had a tragic effect on his daughter. You see, he was granted the ability to turn things into gold by just touching them. But he didn't think about the consequences when he touched his daughter. In an instant, she was transformed into a solid gold statue. His excessive greed for gold led to this horrible outcome, and he was left with a lifeless golden figure of his daughter instead of the living, loving girl he once had.
There could be an ancient evil entity that was sealed away long ago in Vacuo. Due to some recent events, it starts to break free. It corrupts the minds of some of the King's men and tries to use them to get rid of the King and RWBY, who are the only ones who can stop it from fully emerging and causing destruction.