I think that the grandmother may represent a couple of things. I first think that she represents selfishness and manipulation. She is constantly trying to selfishly manipulate her family members. She doesn't want to go to Florida. She wants to go to Tennessee. So what does she do? She tells the family all about the horrible Misfit killer that is in Florida. She says that Florida would not be good for the kids. She says that John must not have much respect for his home state and that is why he wants go to to Florida. Talk about a guilt trip.
Her selfishness is very apparent after she and the family are captured by the Misfit. Not once does she ask or beg the Misfit to spare the lives of her children and grandchildren. She only asks him to spare her life.
She is also a hypocrite. The entire story is about her trying to manipulate people. Her family, the Misfit killer, etc. While trying to manipulate people, she even lies and/or tells half truths. Yet despite those negative qualities, she claims that she is the very definition of a southern lady. Perfect looking at all time, moral, honest, virtuous, etc. She may claim all of that, but her actions prove her a hypocrite.