In "A Good Man is Hard to Find," what are the conflicts of the story?
There are certainly plenty that you can look for in this somewhat disturbing short story, but I will talk about the one that is introduced in the opening of the tale and refers to the conflict between the grandmother and her son, Bailey:
The grandmother didn't want to go to Florida. She wanted to visit some of her connections in east Tennessee and she was seizing every chance to change Bailey's mind. Bailey was the son she lived with, her only boy.
As we read on in the story it becomes evident that the grandmother is an incredibly annoying character who is determined to get her own way, using manipulation, deceit and trickery to do it without any shame. Thus she takes her cat secretly in the car with her, even though it results in an accident. She manages to get Bailey to go off the main road on a spurious trip to visit an old house. Of course, although in this conflict the grandmother always wins, it is ironic that each "triumph" she gains leads them ever closer to their deaths. For example, note that in the first paragraph, she uses the presence of the Misfit as an argument why they should not go to Florida, even though when she is successful and they go to Tennessee they go straight into his path.
So, certainly one of the major conflicts you will want to discuss in this short story is the external conflict between the grandmother and her son, Bailey. In being determined to get her own way she causes him significant annoyance and trouble, and also leads them all to their deaths.
An external conflict in the story is between the Misfit and his gang and the Grandmother and her family. When the family's car ends up in a ditch on a back road that the Grandmother mistakenly thought led to an old plantation, the Misfit feels there's no choice but to execute the family, so he does. This is, to put it mildly, not what the family had planned for as they headed out on their family vacation. The Grandmother is left to face off against the Misfit and try to plead for her life.
But a far more important conflict is the internal one the Grandmother wages. She has spent her life relying on her family, her class (being a "lady"), and her money to protect her. But in a very few moments all that is stripped away: her family is taken to the woods and shot, and she quickly realizes that her being a lady means nothing to the Misfit. She recognizes too that money has no power to buy him off. Stripped of everything, the Grandmother is shown helpless and vulnerable before death, and for the first time truly must rely on God's grace.
The Misfit too faces a deep and wrenching internal conflict: is the story of Jesus true? Is he really the son of God? If so, the Misfit is living the wrong way. If not, nothing really matters. When the Grandmother touches his shoulder for a moment and genuinely sees him as just like her son, the suggestion is that the Grandmother may also have, for an instant, touched his soul.