What kind of relationship did Mrs. Bennet have with her children, especially Elizabeth and Lydia?

Mrs. Bennet wishes for all five of her daughters to marry well. When Mr. Bennet dies, Mr. Collins will inherit almost everything the Bennets own. She wants her daughters to be cared for in marriage. At times, she lacks decorum. She is often loud and indiscreet. Elizabeth is sometimes ashamed of her mother's behavior.  

In her eagerness to marry off her daughters, Mrs. Bennet is overly involved in their lives. She often overlooks impropriety in her two youngest daughters, Kitty and Lydia. She seems unconcerned with their boisterous behavior.

Elizabeth and Mrs. Bennet have a strained relationship. Elizabeth is much closer to her father than her mother. Mrs. Bennet wishes for Elizabeth to find a husband, regardless of how her daughter feels toward the man. When Mr. Collins proposes, Mrs. Bennet "insists upon [Elizabeth] accepting" his offer. She repeatedly tries to "coax and threaten" Elizabeth in an attempt to convince her to accept Mr. Collins. Mrs. Bennet is insistent, even though she does not like Mr. Collins very much. She only starts to like him when she sees he is interested in marrying one of her daughters.

Mrs. Bennet and Lydia are much closer. Mrs. Bennet seems to favor and often encourages Lydia, even if her behavior is inappropriate. When Lydia runs away with Mr. Wickham, Mrs. Bennet is distraught. She had been indulgent with Lydia, allowing her to travel with Colonel and Mrs. Forster to Bath. While in their care, Lydia ran away with Mr. Wickham. When Mrs. Bennet hears the news, she reacts

with tears and lamentations of regret, invectives against the villainous conduct of Wickham, and complaints of her own sufferings and ill-usage; blaming everybody but the person to whose ill-judging indulgence the errors of her daughter must principally be owing.

Eventually, Mr. Wickham agrees to marry Lydia. Mrs. Bennet is delighted to hear the news, and "to know that her daughter [will] be married [is] enough." She is not "humbled by any remembrance of [Lydia's] misconduct." She overlooks that Lydia nearly ruined the family's reputation with her behavior. Once again, Lydia is in her mother's favor.