Since Eliza's birth date wasn't identified, I searched for it first:
The Social Security Death Index:
Eliza K. Aimoku, born 19 August 1914, died May 1992, "last residence" Waianae, Honolulu (Oahu), Hawaii. Her SSN, 575-20-8471 was issued in Hawaii before 1951.
--The "last residence" on the SSDI is NOT necessarily where a person actually
lived or died. The Social Security Administration calls it simply the "home
of record." It is not necessarily where any benefit was paid to the person,
survivor, or the lumpsum death benefit (in 1972 was paid to anyone paying
burial expenses, family member, funeral home, city/county, attorney). It is
sometimes the location where the notification of death was sent to the SSA,
sometimes where the lump sum death benefit was sent.
--If you do not know the names of her parents, she would have identified them on her application for this SSN (at least the persons she identified as being her parents). You can obtain a copy of the actual application.
http://genealogy.about.com/od/online_records/a/ss5_request.h...Your grandfather, from your website: "Paul Hatchie, who's mother was Martha Kuluwaimaka Kapea(or Kapeemu - ancestry and the LSD sites can't determine which one it is)." I'd suggest also obtaining his application, that would also identify who he identified as his parents.
US Census:
For last name: Kahoonei (Kaho'onei), the 1930 Census had a Helen, age 17 at Waimea, Kauai, dau of Peter and Klia. This Helen would have been born about 1912/1913. The 1920 Census did not show Helen.
This Helen is shown in a family tree:
http://trees.ancestry.com/tree/2902704/person/-1803998684?ss...=
The tree shows other females identified as being "private." This term is identified when a person can not be identified as having died. So, it is "possible" Eliza was one of the females. You can contact the owner via Ancestry.com if you have a subscription, if not you might use your library card at your local libraries computer system if they have the library version. But since (Below) indicates you have an account, contact the owner.
--There was a "Private" family tree that DID include Eliza. I sent a message to the owner of this tree to read this thread, help if possible.
---I then found your own "Private" family tree. There is enough information shown to realize the Peter and Klia are probably the parents of Eliza. But, why was she not in the 1920 Census with them? Was she adopted?
The family search org has the birth data of Eliza:
http://www.familysearch.org/Eng/Search/IGI/individual_record...---This identifies her parents as William Moku Kaea Kahoonei, mother Holokai Kamaile Helen (?). Marriage to Henry Aimoku.
--The Social Security Death Index shows a William M. Kahoonei, Jr. born 7 Nov 1914, died 2 June 2000 "last residence" Waianae, Honolulu, HI. If this IS the son of the same man... We have the Hawaiian versus of Arnold Schwarzenegger. I do find this name also on your "private" family tree.
So, it appears you have taken the steps to find this family. Your research would be in HI. Records there are "private" but you being a grandson might have access.