Mrs. Bennet is was not the best mother we can think of in literature. She had a tendency to whine and not fix, to demand and not support, and to complaint excessively in the hopes that her daughters would be have as she wanted them to, in order to land themselves a good husband.
With both Elizabeth and Lydia she acted as only one would expect. Elizabeth is the antithesis of Mrs Bennet in almost its entirety. She is her second child, opinionated, outspoken and resilient in a time where women had to be seen and not heard, tactful and shy. Since Elizabeth did not represent the image of the marriage-able daughter , Ms. Bennet basically had to be what we could say "on top of her" at all times making sure that her behavior, or her tendency to express her mind does not scare men away. However, it is clear to see that Elizabeth was way smarter and witty than her mother, and often ignored her. For this, there would be no punishment ever, and the father was no help in disciplining her either.
Lydia, which was a terribly selfish and quite foolish daughter, also received similar treatment but was always over-protected. However we see how that didn't work because she ended up eloping with Wickham to her mother's great distress and shame. However, as the mother only preocupation was image and status, when Lydia was made to marry Wickham, still we see the little or no influence of Bennet over her daughters' behaviors or destinies.