Not intentionally defending him (or the author's choices), I just felt like a logical debate...sorry lol
Soo-won saved her several times. When she initially escaped, when they met looking for Jaeha, etc etc.
As far as Yona's fears for Hak, I don't think it's irrational. Yeah, they were being hunted, but not necessarily actively. They chose to find the dragons and it meant they ended up in contact with their fairly passive pursuers (we hardly see an active pursuit. Details are left hanging for the readers' imagination to read between the lines...it's often called off, forgotten). It's also less dangerous outside of the palace. They had places to hide and friends who knows who would help them. Inside, they have one (potential) ally. Two, if you consider Soo-won as a possibility). For them, they can't trust him, even if he does decide to actively help them out.
Honestly, I'm pretty sure Kae-sook is their biggest enemy. Soo-won can't reason or come to a deal with anyone if he's unconscious, so yeah, Hak and Yona could be killed iif there is benefit to it. I don't think Soo-won would voluntarily order them killed.
╮(￣▽￣)╭
let me get this right
she feels sorry for soo won who was ready to kill them all this time and had near death experiences because of him...
and now she is worried about hak getting sentenced to death when all this time in their trip he was a wanted man anyways...
she should just go on the run and when he dies then return to take your kingdom(づ￣ ³￣)づ