This doesn't seem to make sense. Although Yona is still young and inexperienced, despite all that they gone through, so not making sense is actually sensible. Nevertheless, someone should ask her what they have been doing all this time. The answer would be protecting Kouka, making right some of the things King Il caused directly or indirectly, defeating foreign enemies, but above all helping the people. What good would be hiding in the royal castle do? They wouldn't be helping anyone there. That's nothing like what Yona has been doing so far. She should realise it. If she goes to the castle, it should also be for a reason similar to what she has been trying to do all along.
Kye-Sook is quite crafty to be using those fear based Sith techniques against Yona, nonetheless.