Perhaps, for whatever reason, Jane simply does not wish to reveal her personal views of the Dixons, Weymouth and Frank Churchill? The foundation for her reserve with regards to the Dixons I have offered the idea Jane may think the questions impertinent but for Frank I have no suggestion. Emma’s questions about Frank do not seem impertinent to me. Emma thinks Jane is hiding reprehensible feelings about Mr. Dixon but while I don’t see any evidence for that it could be that Jane is keeping a secret. Jane is capable per the narrator:

“With regard to her not accompanying them to Ireland, her account to her aunt contained nothing but truth, though there might be some truths not told.” (20)

Emma’s inability to forgive Jane her reserve suggests she feels it is meant to be a personal affront but is there any evidence for it? Emma’s recollection of Jane’s manner was of “coldness and reserve; such apparent indifference whether she pleased or not” (20) but then we learn that Emma routinely exaggerates Jane’s faults:

“every imputed fault was so magnified by fancy, that she never saw Jane Fairfax the first time after any considerable absence, without feeling that she had injured her…” (20)

In her conversation with Mr. John Knightley Jane does not appear cold, over reserved or indifferent to whether she pleases or not. She engages in conversation and willingly explains herself and gives her views. Of course he does not ask about the Dixons, Weymouth or Frank.