LAX is best avoided particularly with children.
I can't remember how much the excess baggage costs are but it might be cheaper to bring over the essentails and with the money you've saved replace the things you leave.
We just managed to get 13 items in all, including a stroller and 2 car booster seats, without any charges.
Depending on whether you are planning a sight seeing trip from Auckland to Wellington then consider flying via the Far East and try to fly direct into Wellington if possible. We flew via Hong Kong (spent a few days there and visited Disneyland) and then onto Sydney (stayed a couple of days) and then Wellington.
LAX is an experience I will not be repeating.
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