Alexandra uses terms for Atticus that range from pejorative to affectionate.
In Chapter 9 Atticus and the children go to Finch's Landing for Christmas, where Jem and Scout are forced to spend the religious holiday with Francis Hancock, their cousin. And, because Scout dislikes Francis, he is eager to tell her what his grandmother (Alexandra) has said about Atticus:
"...it's bad enough he lets you [Francis refers to Jem and Scout] all run wild, but now he's turned out a n****r lover we'll never be able to walk the streets of Maycomb agin. He's ruinin' the family, that's what he's doin'." (Chapter 9)
When Scout asks Francis what he means, Francis delights in calling out the pejorative name again, inciting Scout's anger, especially as she has recently been told by Atticus to never say that particular word.
Later, however, Alexandra softens her words when she realizes the challenges that Atticus has faced in the trial of Tom Robinson. Knowing how conscientious Atticus is, Alexandra is sympathetic when Atticus returns home after the trial is over.
“I’m sorry, brother,” she murmured. Having never heard her call Atticus “brother” before, I stole a glance at Jem, but he was not listening. (Chapter 22).
Scout is surprised at her aunt's use of an endearing term never heard before, and used, strangely enough, after what Aunt Alexandra has said in December.
Alexandra calls Atticus “brother” when the verdict is read.
Aunt Alexandra and Atticus seem to have a somewhat tumultuous relationship. She comes to stay with him during the trial to make sure his kids are raised right and to look out for him. He accepts her meddling, but it sometimes frustrates him. She does not usually treat him affectionately, but when he returns home after losing the trial, she surprises everyone.
"I'm sorry, brother," she murmured. Having never heard her call Atticus "brother" before, I stole a glance at Jem, but he was not listening. (ch 22)
Aunt Alexandra shows her softer side after the trial, when she seems to definitely care about Atticus and his well-being. Calling him “brother” is a show of affection that shocks Scout, because she has never heard any such affection before. She normally just calls him Atticus.
In Scout’s life, Aunt Alexandra is a kind of villain because she wants Scout to wear frilly dresses and act like a lady. Atticus does not appreciate her focus on making them understand their heritage, because he wants them to judge others by their character and not their family. She clearly does care about her brother, and does not want him to be disappointed.