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.