I'm not quite sure that 3 is the Illustrious Order of Te Arikinui Queen Te Atairangikaahu. I have a feeling it is The Order of King Potatau Te Wherowhero, single class exclusively awarded to Reigning Sovereigns. Correct me if I'm wrong, apologies if I am. Were you able to confirm the honours and insignia, if so, where did you received this information?
Kiingi Tuheitia commissioned a companion book to the Orders to explain more on their purpose and potential recipients.
http://www.lucie-blaze.com/11.html
However, this is yet to be released to the general public. Nor have there been any public investitures with a list of recipients including why they received their respective honour. Hopefully this system is made more open with more detailed information forthcoming sooner rather than later.
I believe Kiingi Tuheitia is wearing the Insignia of the Order of King Potatau Te Wherowhero. I can't quite work out all the breast stars, therefore I'm not sure if Kiingi Tuheitia is wearing all 3 of his honours or others he has received. Makau Ariki Te Atawhai (Consort to the King) is wearing insignia of an honour as well.