If Mr Woodhouse was the cause of any such mental problems for Emma the narrator would have mentioned it in her introductions seen at the beginning.

Even if it was, my armchair knowledge of psychoanalysis would tell me that this problem can only be solved at the root - which is Mr Woodhouse.

The situation at home with him would have to change to gradually decrease any pressures which she feels due to him, only then could she move forward on the road to recovery.

A showdown with Mr Knightley wouldn't change the deepseated 'whipping complex' literally overnight, but if her conscience was shaken, it would.

We know that she has this side in her, according to Mr Knightley;

"Not your vain spirit, but your serious spirit. If one leads you wrong, I am sure the other tells you of it."

I think that's what has happened - the other side woke up!!!!

As for Emma not actually apologising, it would have been heartless of her to do so while Miss Bates is actually close to tears about Jane Fairfax.

(twinkling away a tear or two) -- but it will be very trying for us to part with her, after having had her so long, and she has a dreadful headach just now, writing all the morning:

In fact Emma is in complete empathy with Miss Bates and is allowing her to share her sorrow. How could she bring up a topic, which would after all be only a formality?

If Emma had brought up this topic it would have heaped coals of fire on Emma's head. for being so self centred. ;-)