@axelim.sg,
what is your purpose of going to NZ? At the rate you are driving, you will be tired, died tired.
Auckland trip - Auckland is not the right place for dolphins and whale watching. Don't waste your money.
If you want to see Hobbiton and Waitomo, I recommend stay one night in Hamilton to see both. Waitomo is nice, but it is a long drive from Rotorua.
Taupo to Tongariro and back to Taupo, you will be tired. I suggest on Day 8, either stay in Ohakune or Taihape. There is no way, you can take 5 hours to drive from Taupo via Palmerston North to Wellington. Going to Palmerston North is a big detour.
Then your drive to Wellington will be shorter. On the way to Wellington, just about 30 minutes from Samson, there is a Honey factory you can visit.
When you are in Wellington, forgot about the Picton crossing. That is a 7 hour journey to and fro. Unless you want to stay overnight in Picton. Then it is ok.
You can depart from Wellington using SQ. They stop over in Melbourne. That train from Auckland to Wellington could be interesting. But, with your 3 year old, I will not recommend the trip.
If you like wines and visit vineyard, then drive from Taupo to Napier/hasting and spend time there. Forget about Wellington.