CPMaverick

It depends on how comfortable you are driving. NZ roads, even what look like major highways on a map, can be narrow, hilly, and twisty. Some might not enjoy it in a large vehicle, and it will be slower in a motor home than a car. It is tiring to drive in NZ, even though it is beautiful. It is not like driving on major highways in the USA/Europe or even Australia.

I expect a motor home (caravan) will be expensive to rent one-way (especially in high season), and expensive to cross on the ferry with. That would need to factor into your plans. Of course, VRBO in high season will be expensive too. Book your accommodation well in advance, NZ sells out completely in some cases in January.

I don't think 10 days is enough to do all that driving to be honest. It would be exhausting. I enjoy driving and am very comfortable driving on the left... but I would never try this in 10 days. If you had a full 14 days, it might be manageable. But still not a good use of your time in NZ. I understand the desire to 'see' all of NZ by driving from top to bottom, but in the time you have, you can't even see the interesting routes (like the west coast of the south island) because you simply wouldn't have time.

Someone recently suggested a road trip from Christchurch to Queenstown via Arthur's pass and the west coast. That would be about 10 hours and from the bits I've seen, a glorious drive. My suggestion would be to tour around AKL and the north island for 2-3 days, then fly to CHC and take this drive to Queenstown, giving yourself 5-6 days to do the drive. Spend the balance around Queenstown.