Oh my. That really stinks that all this can happen just because of a couple of administrative stuff-ups.
Has the daycare contacted WINZ directly? If they haven't, you could give them your written permission to do so, they fax that to WINZ, and away they go. WINZ don't usually give out personal info without the person's permission. Though it's probably all too late for that now anyway, might be useful just to clear the debt owed to them is nothing more - I can't believe your friend went and told others about your conversation! Was she trying to help, or just being a gossip?
BTW... I think I'd be tempted to shift to Waioru if my DH were there for months on end too. Even though I'd always wondered why anyone would live there! That'd be reason enough for me, I think. Dang girl, you'd better have a good net connection there.