It is obvious that Mrs. Dashwood has more desire to act correctly by their family relationship than either of the John Dashwoods. I wonder if they, particularly Mrs. John Dashwood, thought that was because Mrs. Dashwood did not want to cast aside rich relations?
I do not think that Mrs. John Dashwood cares much for family, for family's sake; for duty, for responsibility (except as the world might disapprove her acting contrary to it), or for the value someone might have irregardless of wealth and position.
It would be normal for someone to apply their own values, or lack, to others. Does that explain the affronting Fanny Dashwood used on Mrs. Dashwood when upset that Edward liked Elinor? Did she think it was a way of warning Mrs. Dashwood that there would be no money in Elinor's ambitions?