Annette asks, "Could you please explain to me the difference between a "Kingdom existing as a matter of law and a Kingdom having its own government in place"?
One is simply lawfully wrong. I wonder if the Queen of England believes she still owns the East Coast of the United States? All overthrows are illegal, in the eyes of the government being replaced. It was NOT an overthrow of the Polynesians, just a change to a better form of government in which Polynesians enjoyed a 2/3rds majority voting block due to who was allowed to vote in the new Republic.  Hint:  Most of the Japanese and the Chinese, as well as the Portuguese, were excluded as only those who were citizens of the old Kingdom were allowed to vote.  This also excluded half of the people that could trace their ancestry back to the U.S.  In 1893 there were less than 2,500 people that came originally from the U.S. in Hawaii, only half were born here, out of about 130,000 total census.