This was enjoyable at first but its far too slow. It's just sort of boring at this point.
"The lost princess had a good head to judge the crown prince and hide her identity but then the westener king... she had no reason to judge based on rumors.
I guess the author cares about the plot rather than to stay in character."
She didn't judge the western king based on rumours though. It's a fact that he killed the mentioned Duke and bloodily suppressed dissent in the Western kingdom. He also showed by his considered actions that she was right not to put any trust in him, especially as if he knew her real identity he wanted to use her as a figurehead and puppet he's as dangerous to her in his own way as Rael. Her behaviour towards him was perfectly in character.