If Harper Lee had written in third person, we would see more of a description of Aunt Alexandra's position and social standing and how it relates to her demeanor toward the Finch children.
During the time that this story was written, women primarily gained social standing through the career and position of their husbands in the community, through church or social work, or through entertaining at their homes.
Aunt Alexandra strongly feels that Atticus is not teaching his daughter the necessary skills required to be a successful woman in the culture i.e. a true Southern Belle. It is obvious that Alexandra cares deeply for the children because she confronts her brother regarding their lack of "appropriate dress" and manners since Scout prefers overalls to dresses. She makes herself available to the family during the trial of Tom Robinson as a caregiver to the children. She upholds her brother's representation of Tom Robinson to her friends at the tea party. In Scout's eyes, this character blossoms for the reader as the climax of the novel is reached and the news of Tom Robinson's death is revealed at the tea party.
We only see Aunt Alexandra through the eyes of Jean Louise Finch (Scout) and are left to form a rather biased opinion of this woman based on the very limited exposure we are given to her character. It is Alexandra's stiff upper lip that Jean Louise adopts in the face of the terrible news.