You are of course right in identifying the way that the author presents the grandmother and, to a lesser extent, her family, in this excellent short story. O'Connor seems to omit nothing from her amusing and unflattering description of the grandmother as she manipulates her family and also displays her own set of prejudices related to class and race. Of course, the reason why O'Connor does this is to profoundly question what makes a "good" person, and we are forced to reject the criteria that the grandmother gives for how we define a good person, which is based on appearance and our family background. However, in the story, she is shown to be obsessed by her appearance, carefully dressed with "white cotton gloves" and a carefully selected dress and hat so that if she died in an accident "anyone seeing her dead on the highway would know at once that she was a lady." Likewise she is racist, describing a black child as a "cute little pickaninny" and suggesting that the naked black child would make a lovely photo.
The presentation of the grandmother, and in particular her own sense of self-righteousness, therefore lead us to the ending of the story, and the epiphany that the grandmother experiences, where the grandmother realises that her own discriminatory views and beliefs make her equal to the Misfit in terms of his heinous crimes. This process of seeing herself as being the same as the Misfit is indicated when she says that the Misfit is one of her "babies," and one of her "own children." Such a moment of sudden self-insight is only possible through the uncompromising picture we are given of the grandmother throughout the tale.
O'Connor presents a deeply unflattering portrait of the grandmother in order to give her revelation and redemptive act at the end of the story even greater gravity and meaning.
In the grandmother, O'Connor creates a character that we sympathize with but do not necessarily "like." She is racially bigoted and pretentious. She is nagging and annoying, and her family barely tolerates her. When she meets the Misfit, her initial response is to pathetically beg for her life and then try to flatter him. She tells him that she knows he wouldn't hurt an old lady, that he doesn't look "the least bit common," that he must come from "good people." At the same time, it is impossible not to sympathize with her predicament: she is a deeply flawed but authentically human person who finds herself in a dire situation in which the only way out seems to be death.
The juxtaposition of the Misfit's character with the grandmother's is, of course, central to the story. The Misfit steals and murders, but is honest, reflective, and non-hypocritical. The grandmother is ostensibly a "good" person, but she lies to her family, holds herself above others, and for most of the story is not even a little self-aware. It would be tempting to morally equate the grandmother with the Misfit, and to say that she is just as "bad" as he is, albeit for different reasons. However, to do this would be to miss the point of the story.
At length, it becomes clear that the Misfit is not going to let the grandmother live, despite her most earnest pleas and entreaties. Suddenly, the grandmother's "head [clears] for an instant" and she finally recognizes the Misfit's humanity. They both belong to the same human family, and if not for the accident of circumstance, he might well have been "one of [her] own children." The notions of faith and spirituality that she had been merely babbling about while begging for her life now take on an authentic meaning. She and the Misfit are united not by some sense of shared "evil," but by a shared humanity, and she understands the moral obligation she has to the man who is about to take her life. Thus, even though she does not begin the story this way, the grandmother dies a good person - a beatific smile on her face just above the bullet holes the Misfit puts in her chest.