What is the nature of Mrs. Bennet's relationship with her children, especially Elizabeth and Lydia?
Mrs. Bennet's relationship with her daughters is not a close mother-daughter relationship. She does not care much about knowing them. Instead she sees them mostly as tools to fulfill her own self-interests. Her one and only concern is to see them married well. One reason is that wealthy marriages will ensure that the girls have fortunes after the estate is entailed and that both she and her daughters will be provided for after her husband's death. The other reason is that wealthy marriages, while increasing her daughters' social statuses, will also increase her own social status.
While Mrs. Bennet is fond of Jane, she makes it evident that her true favorite is Lydia. Mrs. Bennet is only fond of Jane because she is the most beautiful. Hence, she believes that Jane's beauty will increase her chances of marrying a wealthy man.
Lydia is described as a "favourite with their mother." She is tall, with a lovely complexion, and good-natured face. Because she is their mother's favorite she was allowed into society at the age of 15 (Ch. 9, Vol. 1). Mrs. Bennet's indulgence led to Lydia's lack of principles and disgrace.
Although it is made clear that Elizabeth is Mr. Bennet's favorite because of her intelligence and wit, the narrator states plainly that Elizabeth is the "least dear to her[Mrs. Bennet] of all her children" (Ch. 18, Vol. 1). That is one reason why she has no objection to Elizabeth marrying Mr. Collins. Mrs. Bennet believes that he is "quite good enough for her(it)" (Ch. 18, Vol. 1).
Hence, Mrs. Bennet's relationship with her daughters is governed by her treating them as instruments to wealth and social status. Jane is the loveliest instrument, Lydia is her favorite, and Elizabeth is her least favorite.
Jane is the oldest*
In the book "Pride and Prejudice" Mrs. Bennet and her husband have five daughters. Two of her girls are well mannered proper young women. Elizabeth is her oldest and is the most responsible of the daughters. Her mother looks to her to help with the other girls and as a confidant. She has high expectations for her daughter’s marriage. Elizabeth behaves in the proper manner of a young woman of her day.
Lydia is her youngest child. She is more demanding and spoiled. She wants what she wants and will do whatever it takes to get it. She does not follow the conventions of her day and gives her mother problems. She falls in love with a man who gambles everything away and elopes with him.
Jane is her second oldest child. Jane is closest with her sister Elizabeth but loves her mother. She confides mostly to Elizabeth about her loves and losses. She falls deeply in love with a man that the family believes is of good measure but turns out to be in need of funds more than marriage.
Mary is more quiet and reflective.
Mrs. Bennet is a very silly and gossipy woman. She is very different from her older two daughters. Her fuction is to try and find suitable suitors for her daughters.