Depending on where you are coming from in the US you could theoretically route your flight to AKL through YVR, which should still be able to achieved as a United codeshare. This would then put you under the auspices of the Canadian Transportation Act, which does have a mandatory federal airline policy around seating of children under 14 with at least one parent.

https://rppa-appr.ca/eng/right/seati...nt-or-guardian

But for the extra cost and likely time of routing via YVR, you'd probably be better just to eat the seat selection cost and therefore retain some control over your seating if that is something that will cause stress. It's likely quite a small percentage of your overall ticket spend for a group of 5 traveling USA-NZ return, even in economy. Failing the YVR option or paying the seat selection costs - like others have said I'd personally start by phoning the United call center and see if they can do it from their end, try a couple of times with different call takers until you get a result.