Final answer:
John threatens to send the narrator to Weir Mitchell for medical treatment if her health does not improve. The narrator is resistant to the idea as she believes Mitchell's approach will be much like her husband's and brother's, which she does not favor.
Step-by-step explanation:
In the text, John contemplates sending the narrator to Weir Mitchell if her health does not improve. Therefore, the correct answer to the question "To what physician does John, at one point, threaten to send the narrator?" is B. Weir Mitchell.
The section where this is mentioned is as follows: "John says if I don't pick up faster he shall send me to Weir Mitchell in the fall. But I don't want to go there at all. I had a friend who was in his hands once, and she says he is just like John and my brother, only more so!" This indicates that the narrator is reluctant to be treated by Mitchell, as she heard from her friend that his approach is similar to that of her husband and brother, which she finds unappealing.