I am actually well aware that Emma started out arguing a position that was not her own. But at the end, in the argument that I quoted, Emma is surprised at what an illiberal view Mr Knightley has of Frank, and I read that as being her view as much as her opinion that Frank should have come. When JA says To take a dislike to a young man, only because he appeared to be of a different disposition from himself, was unworthy the real liberality of mind which she was always used to acknowledge in him; for with all the high opinion of himself, which she had often laid to his charge, she had never before for a moment supposed it could make him unjust to the merit of another. (chpt 18) she is describing Emma's own thoughts, not any verbal argument that Emma makes. I see no sign here that Emma's opinion is not her own. I think the passage about Emma taking the other side of the question from her real opinion referred to her verbal arguments against Mr Knightley's view, not to her own thoughts.

The line about "very fond of bending little minds" also strikes me as one with a great deal of truth in it, even if it is not Emma's argument. Emma laughs earlier in the conversation though, which makes me think that she is not just acting but has become caught up on the other side.

I will just repeat that I know that Frank should have come to visit his stepmother. What I am arguing here is that Mr Knightley is being prejudiced on the other side - he is determined to think badly of Frank Churchill - not that Frank himself is without fault.