Estella and Miss Havisham are not close. They are puppet and puppet-master more than daugther and mother.
To understand the rocky and unusual relationship between Miss Havisham and Estella, it is important to know their history.
Estella is Miss Havisham’s adopted daughter. She is the child of Molly and Abel Magwitch. Unfortunately, shortly after she was born both of her parents ended up in jail. At this point, her father was deported and her mother was acquitted. Her lawyer Jaggers then sent her to live with Miss Havisham, because the lady was lonely and expressed a desire for a daughter to adopt and raise as her own.
Miss Havisham had been tricked by her brother Arthur and his associate, Compeyson. She thought she was going to marry Compeyson, but he deserted her on her wedding day. As a result, Miss Havisham seems to have suffered some kind of mental collapse. She cloistered herself up in her house, stayed in her wedding dress, and changed nothing for more than a decade.
Estella often refers to Miss Havisham as her mother by adoption. Whether either one has affection for the other is hard to say. Miss Havisham is selfish and cold.
Miss Havisham, you must know, was a spoilt child. Her mother died when she was a baby, and her father denied her nothing. Her father was a country gentleman down in your part of the world, and was a brewer. (ch 22, p. 123)
Arthur was “riotous, extravagant, undutiful—altogether bad” and his father disinherited him, leaving Miss Havisham alone with the fortune. Arthur thought himself ill-used, and devised the marriage plot.
Miss Havisham has plans for Estella. She is to be her instrument of revenge on the male sex. So Miss Havisham raises her to be flirtatious and cruel. She directs her every move, using Estella as a kind of puppet.
When Estella is older, she acts coldly toward Miss Havisham. The old woman is surprised.
“Did I never give her love!” cried Miss Havisham, turning wildly to me. “Did I never give her a burning love, inseparable from jealousy at all times, and from sharp pain…” (ch 38, p. 207)
Estella reminds her that she is everything she was taught to be. She resents her upbringing, and the fact that she was used. Pip accuses Estella of marrying Drummle just to get back at Miss Havisham, but Estella insists she is doing it so that she can make one choice on her own. The fact that it causes Miss Havisham and Pip pain is a bonus.