dad works in NZ and has a visa to be here, I'd hope that the immigration people aren't that stupid. Nix will be onto it for sure.
It's Aussie that's the problem.
Scratch that, sounds like it's the transit through US.
Many nationalities don't qualify for an ESTA visa to the States. Peruvian citizens don't.
Could be a long tricky flight to NZ, as I don't think Canada-NZ flights are operating at the moment, which would normally be one alternative path to avoid Gringoland.
May have to go Mexico-EU-Doha-Syd-Akld or some other nasty route. That's if he and la familia aren't just flying directly to NSW.