Realistically you have 4 days and that is counting your arrival day. Your goals are far too ambitious for this amount of time.
Read a few other threads, it is very common for people to underestimate travel times in NZ and so the advice you are about to receive is repeated over and over again. Just map out the goals you have, even roughly, and you'll see how unrealistic they are. You are considering trying to 'see' Hobbitown, Waitomo, and Rotorua on the first day? That is 6 hours of driving, and not on highways. When would you actually see anything in these places? No need to go into much further detail until you revisit your goals.
My advice for your timeframe would be to fly to Queenstown on the day of arrival, spend 2 nights there and take an excursion to Milford Sound or another spot. Fly back to Auckland and spend the night there, then drive down to spend your final night near the Waitomo Glowworm caves. You have time in the AM to get to the airport from there.