Aunt Alexandra did not approve of the way Atticus raised her children by letting Scout dress and act like a boy.
Aunt Alexandra felt that her brother’s children needed a woman’s touch, since their mother was dead, and Calpurnia was not enough. She seemed to think that Atticus did not inform them of the importance of their heritage and what it meant to be a Finch, because Atticus did not want his children to feel they were better than anyone else.
More than anything, Aunt Alexandra did not approve of how Atticus raised Scout. She wore overalls, was allowed to swear, and ran around all day doing tomboyish things.
Aunt Alexandra's vision of my deportment involved playing with small stoves, tea sets, and wearing the Add-A-Pearl necklace she gave me when I was born; furthermore, I should be a ray of sunshine in my father's lonely life. (Ch 9)
Alexandra cared less about a child’s character, clearly. Francis is racist and mean, and that suits her just fine. All she cares about is the Finch name.
Aunt Alexandra is the quintessential Southern Belle who is concerned about proper manners, values, heritage, and family background, and believes that females should act a certain way. She disapproves of Atticus' parenting style and disagrees with how he allows Scout to dress and behave like a "tomboy." She also feels that Atticus needs to do a better job of instilling a sense of pride in their family heritage. Alexandra even petitions Atticus to teach his children about the Finch family history. In addition to disagreeing with his lack of enthusiasm regarding family background, she disagrees with Atticus' decision to let his children interact with individuals of a lower social class. After Atticus is finished telling his children about how the Cunninghams are respectable individuals with integrity, Scout asks if she can invite Walter Jr. over to play. Alexandra forbids Scout from playing with Walter, and when Scout asks why she can't play with him, Alexandra says, "Because—he—is—trash, that's why you can't play with him" (Lee 137). Aunt Alexandra's reasoning depicts her deep-seated prejudice towards lower class individuals. Unlike her morally upright brother who believes in tolerance and equality, Alexandra maintains her ignorant, traditional views on society.
This is a good question. Aunt Alexandra is a conservative woman who is very conscious about things like propriety and class. So she wanted Jem and Scout to grow up in a certain way - especially Scout. She was worried that Scout was too much of a tomboy and not a proper lady (in Alexandra's eyes). According to Scout, Alexandra was cold. Here is a memorable quote:
"Aunt Alexandra would have been analogous to Mount Everest: throughout my early life, she was cold and there."
Aunt Alexandra was also concerned that Atticus was too lax in his parenting. In her opinion, he allowed his kids to do whatever they wanted. She was also concerned that Calpurnia had too much say and authority over the lives of the children (in the absence of a mother). So, when the kids went to Calpurnia's church, Alexandra did not care for it too much. And when the children wanted to go to Calpurnia's house, Alexandra forbid it.
Here is a quote that shows the tension between Alexandra and Atticus:
"Atticus’s voice was even: “Alexandra, Calpurnia’s not leaving this house until she wants to. You may think otherwise, but I couldn’t have got along without her all these years. She’s a faithful member of this family and you’ll simply have to accept things the way they are. Besides, sister, I don’t want you working your head off for us—you’ve no reason to do that. We still need Cal as much as we ever did.”