domain mapping / cloaking affiliate links

Hello
thanks for reading and i appreciate any help i can get!

my situation is this:
i have built content on mydomain.com
i have set up mydomain.co.nz to mirror mydomain.com

now i have instructions from my client to have ONLY mydomain.co.nzworking and mydomain.com is not to be shown at all.

what options do i have at the moment?

thanks for your help