How we cite our quotes:
So far all was perfectly right; but Lady Russell was almost startled by the wrong of one part of the Kellynch Hall plan, when it burst on her, which was, Mrs Clay's being engaged to go to Bath with Sir Walter and Elizabeth, as a most important and valuable assistant to the latter in all the business before her. Lady Russell was extremely sorry that such a measure should have been resorted to at all, wondered, grieved, and feared; and the affront it contained to Anne, in Mrs Clay's being of so much use, while Anne could be of none, was a very sore aggravation. (5.11)
It's just incidental to Lady Russell's objection that Anne is more competent and reliable than Mrs. Clay – what really burns Lady R.'s pastry is that Elizabeth is choosing someone outside the family.
She acknowledged it to be very fitting, that every little social commonwealth should dictate its own matters of discourse; and hoped, ere long, to become a not unworthy member of the one she was now transplanted into. With the prospect of spending at least two months at Uppercross, it was highly incumbent on her to clothe her imagination, her memory, and all her ideas in as much of Uppercross as possible. (6.3)
The family is like society in miniature, and it's here suggested that, to be a good family citizen, one must conform, to the extent of becoming almost a different person (because between "imagination," "memory," and "ideas," that's pretty much a whole identity right there). Though Anne thinks this at the beginning of her stay, it would be interesting to look more closely at how she lives up to her initial plan.
"You know," said she, "I cannot think him at all a fit match for Henrietta; and considering the alliances which the Musgroves have made, she has no right to throw herself away. I do not think any young woman has a right to make a choice that may be disagreeable and inconvenient to the principal part of her family, and be giving bad connections to those who have not been used to them. And, pray, who is Charles Hayter? Nothing but a country curate. A most improper match for Miss Musgrove of Uppercross." (9.13)
"Think of the family!" is the "think of the children!" of this novel – the statement characters can use to shoot down any plan they don't like. Here Mary uses it to defend her selfishness in putting her own snobbery ahead of Henrietta's marital happiness.