Dowun is problematic, agreed; but no one can deny that his tactics had results.
You can prefer Baek Han all you like; he was nowhere to be found when Dowun put his neck and even his family on the line to drag her to the pinnacle for her own (and his) benefit, kicking and screaming if need be.
Her highness can be as upset as she likes. Anyone can see that she was very likely to have been maimed or outright died long ago to some petty, offhand scheme of her numerous royal siblings without Dowun's continuous intervention.
I wonder if some readers really know how life works. Very few people do things out of altruism; selfish interest is a normal motivating factor in human interactions.
A mutually beneficial, selfish set of actions is not grounds to subtly sulk. Her elevated position doesn't insulate her from danger.
I believe this may be what Dowun is trying to get her to understand, as her position affects his own.