"About a year ago she was taken from school, and an establishment formed for her in London; and last summer she went with the lady who presided over it to Ramsgate; - Chapter 35
In his letter to Elizabeth, Darcy speaks of an establishment being formed for Georgiana, and presided over by Mrs. Younge. He does not say she and her companion resided at his home in London, he writes of it being a new place - at least that is how I read the word "formed."
I do not see him allowing any companion of his sister to to preside over his home, but he does state that Mrs. Younge presides over the place Georgiana lives.
In my Annotated copy of P and P, this is what the note about this quote says: "
establishment: household, residence. Living in London, instead of returning to Pemberley, could allow Georgiana to further her education, for London would have the finest masters to tutor her; it could also allow any close friends of the family who lived in London to introduce her to more people and thereby help improve her social skills and extend her network of acquaintances."
As I read this, she did not live with her brother, but with her companion, and the purpose of her being established in London was to further her education.
