Aunt Alexandra moves in because Atticus is so busy with the Tom Robinson case. She feels that Calpurnia is not suitable to be a good parent. Aunt Alexandra wants to install some old fashioned gender roles in Scout and keep them from "running through the streets". Aunt Alexandra is a product of her background. Unlike Atticus, she missed the bus to education and enlightenment. She certainly seems like most women in Maycomb and to an extent she is. She has the racial prejudices and a penchant to be judgmental. These, however, are tempered with an understanding that her brother is really a good man and father. She seems to realize deep down that Scout and Jem are wonderful kids and lucky to have a father like Atticus. This is not so much stated as implied. I'll include two quotes representing both sides of her.
"Aunt Alexandria had boarding school manner; let any moral come along and she would uphold it." Ch 13
The other side of Aunt Alexandra does not show up until later chapters. After Atticus explains Tom Robinson was shot Scout says, "I thought Aunt Alexandra was crying." Ch 24