>People of their class socialised because ti was what they did.

But Emma didn't. She didn't socialise. She stayed home most of the time. To expect her to change her ways just because Jane was visiting, who really didn't care, is unrealistic. It ould be different if they had shared a warm and friendly relationship.

>since Jane was by gentry standards very poor, it was also Emma's duty to show her some "attention" to mitigate the effects of J's poverty.

I think Jane could do without the riches for the short time she would be in Highbury. It would show a strength of character to experience what her aunt and grandmother did. After all it wouldn't be for a long time. Only as long as her visit lasted. Then she would be back in London. They were only gentry poor, not 'poor' poor.

As for Emma, she did a lot for the really poor.
She did invite Miss and Mrs Bates to Hartfield, even if it was for her father's sake. Jane was not there most of the time. She was in London.

>"always doing more than she wanted to do, but less than she ought".

Emma ought to do this, but she didn't like Jane (and surely vice versa). If she did this, she'd have been a real saint. And saint she wasn't, her attitude towards Jane was very normal, very human.