JA provides explanation concerning why the Coles did not invite the Woodhouses earlier (for, as we know, they did invite them finally). The Coles expected a folding screen from London, to protect Mr Woodhouse from any draught of air. In the quote you mention, Mrs Weston adds "they know you do not dine out". If the Woodhouse do not dine out in general, the Coles can hardly feel slighted in particular.

As for Emma snubbing Miss Bates and Jane Fairfax at the Coles' party, I have to disagree because, first of all, we have no text at all about Emma's interactions with Miss Bates. The text you quote refers solely to Jane Fairfax, so it is hardly fair to conclude that Emma did not dive a smidgeon of her attention to her father's life-long friend" etc etc. Concerning Jane Fairfax, Emma kept a distance at the point you mention because she did not wish to speak about the piano-forte, the topic that was currently being discussed. It had nothing to do with lack of condensation. Personally, I do not apporach everybody in large parties- I approach my friends- and I do not think this is the same as a snub. I feel we have come to a point where Emma is expected to like everyone and be everywhere at the same time, just because she has a high social standing.

I agree that Harriet, most probably, did not introduce Mr Martin to Emma (a possibility I was pondering on). I do not feel it was a snub (or ungracious) for the reasons already stated in my post above.