I was going to suggest Peru, but you said Australia/NZ is too cold, and Cusco may very well be colder. IMHO, winter is a good time to visit if you're okay with the cold. Ther is plenty to do in Peru for 2+ weeks, and you may even be able to use the voucher on some internal flights on LAN/LATAM.

Edit: how old are the kids?? There is a big difference between 4 year olds and 12 year olds.