I thought Emma had
realized that Regina killed Graham, but looked past it because that's what she'd
like to do to a man who cheated on her.
Snow White isn't the one to really articulate this, but her father was a lousy husband to Regina. Morally speaking, that just gave Regina grounds for divorce. But in monarchies divorce is a life threatening, often life-taking proposition. Plus, ruling monarchs, being divine by blood, don't really get to resign, since they can't undo their own flesh. They're more or less forced in it til the death.
The oppressive Queen thing is really part of the job description. The notion that Charming and Snow White rule by inspiring unbridled love and radiating happiness down on the peasants has got to be the biggest fairy tale in the whole series.
No, the really hideous thing Regina did was sacrificing her father. Which is why "Henry" became so important?