If it doesn’t have all these codes, then pick up your bag in the top airport listed on the bag tag. Most likely, that will be LAX because I’m really not sure if HP (America West) will automatically tag bags for Air New Zealand or Qantas.

If all are listed, then pick up your bag in Auckland, New Zealand. This is where you’ll clear NZ Customs. Most international airports require passengers to get their luggage and present it for inspection when first entering a country. Once you clear Customs in NZ, there will be an area to re-check your bag for the flight to PMR.

The only reason you’d have to pick up your luggage at LAX is if America West didn’t tag the bag for the New Zealand leg of your trip.

If your NZ flight number is listed on the bag tag, just walk out of LAX Terminal 1, make a right when you hit the street, and walk either to Terminal 2 (Air New Zealand) or to the Tom Bradley International Terminal between Terminals 3 and 4 (for Qantas and Air Pacific). There’s one UA flight at Terminal 7 that goes to NZ also.
References :

For other circumstances (longer stay, non-visa free country) see: http://www.immigration.govt.nz/migrant/stream/visit/

Even if she doesn’t need a visa for her designated stay, if she stays on beyond the departure date she has given to immigration upon arrival, she will be in breach of her visiting conditions.

EDIT:
One other point. As she’s a minor, the NZ immigration authorities will need to be satisfied that she will be adequately cared for in a safe situation. She should take a certified document from her parent or guardian giving permission for her to stay with the family in question. It should include a date up to which the permission is valid.
References :

They may offer flights from Singapore or Malaysia into Auckland but im not sure.

If they dont…here are the 2 best alternitives.

Fly to Hong Kong with anyone. Air New Zealand then flies from Hong Kong straight back into Auckland-non stop.

Or go via Australia. I recomend Singapore Airlines into Sydney and then Air New Zealand into Auckland, Wellington or Christchurch.

Singapore Airlines and Air New Zealand are in the ‘Star Alliance’. That means nothing to the joe average traveler except for that it is easier booking flights when going through a Travle Agent (HIGHLY RECOMENDED!) So if the Singapore flight is delayed…Air New Zealand may put you ahead of the others onto the next flight because you flew with a partner airline.
References :
my dad has been there, done that with Qantas/American airlines (also in an alliance)