Suggestions for itinerary mid Dec

Hi, We are family of 3(two adults, one three years old) travelling to NZ for the first time in mid Dec.

We plan to focus North. We have about 2 weeks. Objective is primarily scenery; we're not into adventurous or water activities such as rafting and challenge hiking

We'll self drive.

Here is our itinerary:

Day 1: Arriving Auckland from Singapore 2pm (planning 8th Dec). Rest for the rest of the day

Day 2: Explore Auckland City proper

Day 3 Explore Auckland surrounding or island

Day 4 Travel to Rotorua 8AM (via Matamata for Hobbiton movie tour)

Day 5 Explore Rotorua (planning 2 geysers/thermal attractions)

Day 6 Explore Rotorua (nearby attractions or join Waitomo day tour)

Day 7 Travel to Taupo (planning Waimangu and Wai-O-Tapu)

Day 8 Explore Taupo

Day 9 Travel to Wellington 8AM (5 hours)

Day 10 Explore Wellington city

Day 11 Explore Wellington surrounding

Day 12 Fly domestic back to Auckland (maybe if schedule allow train)

Day 13 Fly out of Auckland (12pm)

My concern is Day 9 onward, worth to spend 5hrs drive straight to Wellington?

Should we skip Wellington all together and focus on places before Taupo?

Thanks in advance.