First, she doesn't have all the money and resources yet to survive elsewhere.
Second, until the "real daughter" is found she believes she is still needed to be a stand in. If she were to run now they would chase her and she wouldn't make it far. She needs a big distraction. If she runs after it's announced that the real daughter is found then no one will be looking for her. It'll give her enough time to just disappear.
Third, this world is built like a game. A function of that game is that she needs to maxout someone's affection for her to be safe. Of she doesn't then there are strange ways that the world will try to kill her, even if she runs. That's why she focused so hard on Eclipse. She needed him to love her and run away with her to both keep her safe and satisfy the demands of the world.
Why do you make it sound like it's easy to just run off
She is trapped in a Game. I don't think fl running off from the Duchy would help free her and return to her world.
I don't understand why the Fl is still in that fucking Duchy? Why doesn't she run away