Quinn moved away from the throne after Floid dismissed her and stood at the bottom of the stairs. It was obvious that she was still angry about what Floid said to her. She believes that she deserves a second chance to find Dray. It isn't her fault that Dray wasn't in Uta.
But Floid is not going to indulge every little request from the people under him. Feed your pets too much and they will become dependent. If Floid granted Quinn another chance, she will never learn her lesson.
Quinn has to learn to think thoroughly before taking action. Floid knew Quinn was a very smart woman. Quinn would not have survived under their father for so long if she wasn't smart, but Quinn allows her emotions to rule her judgment too much and that has led her to make many bad decisions since she came here. That is one of the reasons why it was so easy for Dray to fool her. Quinn must learn how to think without allowing her emotions to take control of her.