If there plan is to go to Australia, and they only have 20 days (less flight time?), then forget the "free" stop in Auckland and spend all of the time in Australia.

If they had planned to go to New Zealand and had a free stop in Sydney, I would suggest skiping Australia and spending all the time in New Zealand. In New Zealand, 20 days would give your parents a fair chance to see most of the country.

In Australia, 20 days is a very short stay. WA can be done in 20 days. Melbourne and Adelaide can easily be done in 20 days. Sydney and Caines can be done modestly in 20 days. I am hoping to do Brisbane and Tasmania in 20 days but seem to need about 3 more. Naturally these time periods are based on thing, we like to do. It is what your parents like to do that counts.

Tours are available to do "large areas of the country" poorly, IF this is the only trip your parents will ever make to Australia. If this is one of several, then I would suggest consolidating the time in as few cities as possible.

Lots of great web sites exist. With a lot of effort and time, your parents can find what things they would like to see and do. That is the way I plan our trips. Then, where and how long will become much easier.