One thing I thought to examine were the women around Anne, the centre of the story. I notice at Uppercross, Anne is 'known to have some influence with her sister' (ch.6) so she's continually sought out by family members who ask beyond what is practicable with Mary.
I think Mary may have been a more amiable person if she did not insist that Mrs Musgrove 'give her the precedence that was her due when they dined at the Great House with other families'.
My impression is Mary prefers to remember she is the daughter of a Baronet than a member of the Musgrove family.
Mary's little obssessions appear to cause concern within the family. Hence, they confide in Anne to give Mary a hint not to take precedence over mama, or persuade Mary not to fancy herself so ill or ask Mrs Charles to manage her children and servents better. By contrast, Mary complains to Anne she is not given her due.
I'm not sure if these are small domestic grumbles or more serious concern. Anne listens and 'give them all hints of forbearance necessary'. I think her relations at Uppercross had more confidence than her family at Kellynch but may've somewhat over-rated her influence with Mary. Apart from seeing Anne as a sympathetic sister whom she could confide her ailments; I doubt Mary is really influenced by Anne or she may've been a happier person.
I maybe rather hard in my assessement of Mary; Potentially, she may've been a better person. I know she was married and had children at a young age and lost her own mother when vey young.