Lady Middleton is...

chilly, polite, and impersonal (contrast to Marianne's spontaneity and warmth)

self-centered, insipid, intellectually limited (contrast to Elinor's thoughtfulness and interest in other people)

negative portrait of a woman in the maternal role - only focused on her children (contrast with Mrs Dashwood's warmth, hospitality, friendliness)

When Austen sums them up with "Sir John was a sportsman, Lady Middleton a mother. He hunted and shot, and she humoured her children; and these were their only resources," I think she is caricaturing the traditional family and traditional male and female roles.

Society thinks it's enough for a man to hunt and a woman to reproduce, and hunter+mother=family. But Austen's main characters will not be satisfied with that, they want richer lives and richer relationships.