What is the conflict between the grandmother and the Misfit in "A Good Man is Hard to Find"?

As a Roman Catholic, Flannery O'Connor was often concerned with the cardinal sins, especially that of pride in her stories.  In "A Good Man is Hard to Find," the grandmother prides herself upon being a lady and a moral one at that.  Hints of the conflict between her and the Misfit appear early in the story when the grandmother takes such care in her dress for the road trip.  She contemplates what a person would perceive if the family has an accident on the way.  With dramatic irony O'Connor writes,

In case of an accident, anyone seeing her dead on the highway would know at once that she is a lady.

If she is killed in an accident, it will little matter what she looks like, yet she is worried about physical appearance and what class people will put her in based upon this appearance.  Later in the story, the grandmother tells her grandchildren that she should have married a Mr. Teagarden since he was a "gentleman," and had died a wealthy man.  Again the grandmother's emphasis upon class and money is stated with death, a context which causes these shallow values to appear foolish.

In the climax of "A Good Man is Hard to Find," the grandmother foolishly does not admit that she is mistaken about the road they travel on to see a house; she also causes the accident because she has smuggled her cat into the car.  After the Misfit and his friends arrive, she does not exert much effort toward saving her family other than trying to convince the Misfit that he is a decent person:  "I know  you're a good man," she tells him.  However, the Misfit disagrees and responds to her recitations about Jesus by telling her that he cannot believe scripture; he can only believe if he has witnessed saving grace.  And, ironically, it is in witnessing this grace in the grandmother as she reaches out to him, declaring, "You're one of my children" that the Misfit shows the potential for salvation after witnessing this Christian reach to him even though he does shoot her: 

It's no real pleasure in life, [killing]

he says which indicates that there is the potential for him to change. 

The conflict within the grandmother is that she does not realize her sin of pride, but in her dying moment she has an epiphany in which she realizes that she is no better than the Misfit:"Why you're one of my babies!  You're one of my own children!"  In a moment of saving grace, the grandmother reaches out to the criminal, humbling herself.