Status match? Do you have AA or other status that you can match? With Star Alliance gold status you would get access if you are headed to AKL.
Another alternative worth mentioning is the Air Canada Lounge Pass. It's priced in CAD and cheaper than buying a UA club membership outright (roughly $370 for the single membership). Downsides include - need to fly Star alliance for access (unlike the UA club where you can enter at any time), and unclear /lack of guest policies. If you fly a lot and this is a one off trip with your family, it may make sense to buy this membership plus one day passes (depending on how the agent requires it) - but the united club credit card seems to be the way to go.
On the amex route - it should be $50 a person if you have any Amex. Much nicer, but crowded lounge but if you don't need UA assistance it would be my recommendation on how to spend the time.