her father.

"She was not a woman of strong understanding or any quickness; and with this resemblance of her father, she inherited also much of his constitution; was delicate in her own health, over-careful of that of her children, had many fears and many nerves, and was as fond of her own Mr. Wingfield in town as her father could be of Mr. Perry. They were alike too, in a general benevolence of temper, and a strong habit of regard for every old acquaintance."(Chapter 11)

They are both devoted to each other, but also both devoted to their own apothecaries--neither wishing to allow any lack of respect to the pronouncements of his/her own medico. They are also probably equally likely to put their own thoughts in their apothecaries mouths. Mr. John Knightley could have been more gracious & just laughed off the disagreement instead of entering an argument--but then we wouldn't have the fun of watching Emma & Mr. Knightly doing tag team diplomacy.