No, "hauaiki" isn't even a word in the Niuean vocabulary. I asked my aunt who was born and raised in Niue and she said it's not Niuean. And "Avaiki" is that cave I posted a picture of in my previous post.
I'm not really in the mood to go and find the word in the Niuean language text that I did. I just made a mental note of it because I would have expected it to have been Havaiki. Hauaiki is a word transliterated from Maori - how old that transliteration is, I don't know. I'm not a modern Niuean language specialist but my hunch would be that a (or some) speaker(s) of Niuean when trying to talk about the last point of origin of Maori, instead of using what word equivalent that existed in their lexicon they chose to transliterate. That transliteration then would have wound up in print. It could be that your aunty isn't a part of the speech community that transliterated the word.
People on Niue wouldn't be talking about Maori origins.
Now that you mention that it was probably an educational book written in the Niuean language to be taught to native speakers of Niuean as a requirement of the New Zealand curriculum where the subject of Maori and their relationship to Aotearoa is taught as a compulsory component on the curriculum.
And since you were discussing cognates for Hawaiki you should have mentioned Avaiki in Niuean.
There is no need to mention what the cognate is in Niuean because I was discussing evidence given from Eastern Polynesian languages - something that Niuean clearly isn't.
you forgot Havaiki/Havai'i in Fakarava.
If you meant Tuamotuan then yes I did neglect that but that doesn't add or change to what I said before it only gives more evidence. I don't quote Tuamotuan as much since there isn't a lot of Tuamotuan that has been written that is easily accessible in Eastern Polynesian outside of French Polynesia.
I'm guessing that you are solely basing your information on a word recently created at New Zealand universities to distinguish the Niuean Avaiki from the Maori Hawaiki?
The study of Niuean language in NZ is not done at University level. That's because it is a very unpopular language which I think is a big shame. I don't think academics would bother creating another word for it unless if they felt strongly and the community felt strongly that there was no connection with Hawaiki. Words made by academics that the community feels that there is no need for ultimately die.
Attitudes towards Niuean language by non-Niueans non-Polynesians and by some young Niuean themselves means that the language will die if there is no attitude shift. I don't think the NZ Govt is doing enough to promote Niuean as a living spoken language. There is a hell of a lot of work to be done because the language is going to die.
Out of the five major Polynesian languages of New Zealand (New Zealand Maori, Cook Islands Maori, Samoan, Tongan and Niuean) Niuean is going to die due to the frantic scramble to learn English at all costs. Cook Islands Maori will die as well as people don't see a need for it despite the fact that to function in the Cook Islands culture Cook Islands Maori is a must. New Zealand Maori is going to survive and recover. Samoan could do better but after two to three generations fluency in the language really deteriorates. Tongan is fine because speakers of the language tend to work in the same line of work and the only way to communicate in the community is to speak Tongan - English is not an option.
The NZ Government has a duty to protect all Polynesian languages under its influence (which then also includes Tokelauan) through promoting education policies that encourage -
1)Receiving an education in the L1/heritage language of the student
2)Encouraging multi-lingualism - for Polynesian students that means a study of other Polynesian languages to complement their L1/L2 language.
3)Encouraging employers to allow their workplaces to be multi-lingual - employees should not be warned for speaking a language other than English
4)Making Maori compulsory to learn as a L1/L2 language from pre-school to university.
5)Adequate funding to restore Moriori.
I think if the NZ Govt does the above I think we can easily turn around the current language situation for Polynesian languages spoken outside of Chile, French Polynesia, Hawai'i and Melanesia. If we protect these and promote them then the others will follow.