I mean would they really let her leave just like that? Even if she promises them money? She has the power to punish them. They'd rather sell her than return her.
Oh damn I forgot about slavery, but still the best way for them to get easy money would be for them to accept her offer, she could even spin the story for them and tell king that they saved her, and offer them jobs or something, still killing him and escaping quietly would be the best option, since he was on the run he probably wasn't able to hire a lot of goons, escaping should be easy.
They practically launched a terror attack around the whole castle so I'm guessing he has plenty of goons. Though he's disabled it'd still be risky to kill and run because she doesn't know her situation or where she is. Plus, no one's dumb enough to let person go who has seen you or knows about you.
She'd have a much better chance at escaping by waiting for rescue and knowing she has back up, or comply with his deal, collect evidences against him and look for the correct opportunity to expose him.
There's also the choice of sacrificing herself for the greater good and killing him.
Didn't he said that there is problem with his resources? Plus there is rly no need to have a lot of men to launch terrorist attack, just selected few in strategic places.
But you are right is quite risky to attack him while she doesn't know where she is, but if she could play along for a while to understand her surroundings and check how many men are there then she could then easily go for his jugular in convinient situation.
Plus since he is trying to frame Rud, waiting for help could take a while, also she doesn't rly need to look or gather evidence, she is a royalty, her word is good enough.
Few chapters ago I was furious why during royal family meeting she didn't say anything about him, it was a perfect moment, he was even trying to find her room in the palace, so she should have said something, if she did this whole situation could be resolved instantly, her overprotective grandpa would strengthen the security, and order a few knights to guard her specifically, and even if she still was kidnapped, they would know who was behind it, and rescue could arrive much quicker.
You have a point that she could have let the Grandpa know.. But I guess she didn't think of it as that much of a big deal because ultimately his goal was the Winterwald and she didn't really have a major role to play in his schemes. However, now he's trying to use her for that railway concession.
In Her shoes I would agree to his conditions, and when he unties me I would attack his blind spot, and killed him, as for his goons, either quiet escape, or just offering them money, since their boss is dead they might comply.