Jane’s playing and singing in addition to the irritation caused by her aunt’s letter reading and incessant chatter.

I don’t see this happening in childhood when Jane had yet to become proficient.

I don’t see Emma beating up Jane or not sharing her dolls and toys. Emma has a very cheerful nature, and Jane likes mischievous and liveliness in a person.
Emma must have been fun to be with as a child I should think.

Here Jane’s thoughts would be useful. Did she feel superior as a ‘city’ girl during her visits? Did she feel envious too of Emma’s situation in life, while growing up?

The bolded letters are all Emma's thoughts, and seem to me like expressing resentment or regrets about things of adulthood.

Emma judges herself very severely and with some exaggeration which is typical of her, like those moments where she tends towards saying “..all my life” quite often, whether it was blushing over a misdeed, feeling ashamed etc or even thinking it a sin to *think* of marrying.