Its not unreasonable of them to want to run away, but if they actually try to, they're just being stupid. They're only little kids regardless of their mentality and they clearly possess features of the royal family. They've experienced a dangerous attack in the Palace but at least they were protected. Now they just want to go and put a target on their own heads by running away. Its not even as if they're living a bad life in the Palace, its just that they don't trust anyone and hate on the rest of the royal family because of misunderstandings due to their family members all being emotionally inept and acting stupidly.
is save for them to stay at the palace
To be fair after all they've gone through i don't think its that unreasonable to run away...