It IS sad for your DD but these things do happen, not always because of the child's parents though!
And FWIW I think you did the right thing by asking the school to intervene on the the "teasing" - judging by the woman in question's responses so far, I doubt she'd have accepted that her DS did ANYthing wrong in the first place. It's always best to let the impartial authority deal with this stuff and she's been very foolish not to realise that.
Hope your DD has a lovely birthday and party anyway!
Unpleasant situation and I can't believe the other mother would be so petty but I would say (sorry) that you have to leave it. She is being pretty mannerless by not RSVPing at all but I gather that's fairly standard these days from a lot of parents, judging by the number of threads on here about it!
I would manage your DD's expectations NOW that Audrey is not going to make it. After all, the woman told you last year that Audrey was never going to be able to come to your house for a playdate - she doesn't sound like the type to forgive and forget from what you've said so far - so just accept that Audrey is not coming. You've done the decent thing by inviting her - the mother has snubbed you - let it go. Sorry for your DD but I don't think you're going to achieve anything by a further email except to further piss her off by "harassing" her.