She's not armed. So if she wanted to protect her father, she would have to go back to her room for her sword. She wouldn't be able to borrow one from the guards since they'll need every sword they can get. Then she would have to rejoin the battle but she'd see her own palace guard turning on one another which would be all kinds of horrifying for her as she realizes that this is a coup. It would mean she'd have to fight her way into the Throne room though; not that she would be too upset about that. And then we can have her be sent ahead and all that.