canaan:”what do the laws say about getting a Hawaiian BC for a child from another country adopted by a Hawaiian citizen?”
This all depends what you want to accept as valid. If the Certification of Live Birth posted on factcheck.org is valid (which is yet to be definitively proved), you have to contend with the location of birth as Honolulu. As far as current Hawaiian law states, a new birth certificate is issued for an adopted child but only the parents would be changed from the original BC. The date and location of birth would be preserved and the original BC is kept (and sealed).
http://www.capitol.hawaii.gov/hrscurrent/Vol06_Ch0321-0344/HRS0338/HRS_0338-0020.htm
Also, for the case of foreign birth, the following link shows (by current Hawaiian law), that the country of birth is preserved on the BC.
http://www.capitol.hawaii.gov/hrscurrent/Vol06_Ch0321-0344/HRS0338/HRS_0338-0020_0005.htm
If you believe the BC on factcheck.org to be fraudulent (likely), then almost anything could be true of the original.
From the comments about an article on Alvin Onaka we know that DOH in Hawaii regularly changes information which is on original vault copy birth certificates in their possession. I will include the article link here and advise to read the comments associated with the article, pay close attention to the first 17 comments.
http://archives.starbulletin.com/2008/07/14/news/story07.html