What she's doing makes sense though, as the prince has no power (not even to protect his child wife) and the queen reigns supreme within the palace. Whether she likes the prince or not, if she angers the queen she's dead. She's choosing to be a double agent instead: give the queen just enough information that she's counted a valuable asset, while strengthening the position of the prince. Eventually, the scale will tip and the queen loses her power, and she can use everything she knows about the queen as a weapon for the prince to use.
The only real question is if the author is gonna do that annoying thing where the prince and princess have "misunderstandings" because the princess stupidly hides information she should have told. I hope that's not how the author does it. The real drama should be in constantly escaping the queen's suspicion and supporting the prince, not fighting with the prince over her being stupid.