mangoguava given that only one uni is asking for international fees, I would say that there is a rebuttable presumption that #2 has got it wrong, and that the decision should therefore be reversed.
It also seems to me that #4 is going to lead to unhappiness, so should be ruled out of count (or rather, that's the approach I would take if this were my own DC).
It seems to me that since your DD's exams are over she could now usefully channel her energy over the next few weeks into insisting that #2 looks again at all her evidence and gives you a properly considered response. I would certainly ask them on exactly what basis they don't consider her a home student - which part of the evidence falls short - and would make the very strong point that they are alone out of all her choices in coming to that conclusion - so she has a right to a full response. #2 can't withdraw the offer so there's little to lose by being insistent.
You have a perfect right for it to be re-addressed at the highest level within the uni (and beyond - but leaving that aside), and so by the time the IB results come out your DD will be in a better position to consider a re-application if her results are good. If they are as good as predicted, and #2 has reversed its decision, then it's extremely likely that they would re-offer next year and you'd have the home status decision to wave in their face if they tried it again. If they stick to their original decision then a re-application to Oxford and elsewhere would have more point.
I would think it highly unlikely that the LNAT score was a fluke. That sounds more like a DC being ground down and worried than it being a real thing. If it was easy to fluke, top unis would't set so much store on the scores. Also, her Oxford feedback suggests that she mirrored her LNAT at interview.
A bad IB - different issues. But she was predicted nearly full marks you say, so here's hoping.