In "A Good Man is Hard to Find," southern gentility is presented as snobbish and ignorant in the character of the grandmother. She idealizes the old south, looking down on racial minorities and dressing up so that if she dies, people will "know she was a lady." Appearance matters more than substance. In regards to its relation to violence, ignorance is once again the keyword: the grandmother seems unaware of anyone else's pain in the world until she encounters the Misfit.
Faulkner's "A Rose for Emily" presents southern gentility itself as quite capable of violence despite its manners. Emily Grier is the last remnant of the old southern aristocracy in her town and the best word to describe her is entitled. She feels entitled to not pay taxes, and when her northern lover, Homer Baron, makes it clear he plans on leaving her, Emily feels entitled to him as well. Her murder of him is her way of making sure she will get to keep and control him.
In both cases, southern gentility is presented as snobbish and outmoded, a relic of the past, but their relations to violence are slightly different. The grandmother turns a blind eye to violence while Emily can get away with murder because of her class status. Emily is cushioned from the impact of her violence, while the grandmother comes face-to-face with death itself (though unlike Emily, she receives a moment of grace and redemption).