I have in the past on long long haul booked and paid for a third seat when two of us were travelling. I've only done it when the seats were pretty cheap of course but it was usually more comortable and cheaper than two seats in old style business class. So I'm not sure that an airline can just dump another passenger in a seat that's been paid for by another. I reckon at the worst you'll have three seats between the two of you.
So if Air New Zealand, which is a great airline, will be compassionate, get a refund, take a friend or, just turn up with a blow up doll, bought from a sex shop and check him or her in(probably her I suspect) as Mr Dexter5. You might have to camp it up a bit as a lesbian but then you'd be providing your daughter with a story worth telling for the rest of her life.
I hope you have an excellent holiday and get through this difficult time with panache and the odd kiwi fruit.