I recommend freeing yourself from your driving option and taking the kids to the Royal Albatross Centre in Dunedin:
https://www.tripadvisor.ca/Attractio...th_Island.html
The blue penguins are very rare and only come ashore at night. So the kids need to be patient. The moment you see them waddle ashore is truly special. The centre has a large viewing area i.e. you want to time your visit @ sunset. Dress the kids well, as you will be on the viewing platform for 30 + minutes.
FYI, we did (with kids) # hikes in the area to see yellow penguins, whales, dolphins and seals - but the Royal Albatross Centre is the place to see the rare blues.
To take the edge off the high price, I recommend you monitor (early and often) the following site where we found sell off discounted tix:
https://www.bookme.co.nz/
The Centre is a non profit and proceeds go into research and preservation.
NB If this does not work, the Centre also has a family rate.