Iʻm not sure how to understand this sentence. Is it meant to say that Kaʻiulani is "a part/member of the family"?
Actually, "X is a Y" in English is "He Y X" in Hawaiʻian. Hence DouglasJulien's confusion. "Family" in the English sentence is an adjective and can't receive an article, so the Hawaiʻian sentence wouldn't make sense if translated word for word.
So this is like, "Do you know Maria well?" "Oh, yeah, Maria is family!" (which either means she's a member of the family or that she's just like she is)? At first, I thought it meant that Ka'iulani was a word for family, but I knew that family was ohana, so that probably wasn't it.
For that sentence, "He" (placed in the front) is treated as "to be".
Kim is family. Kim is a family member. Kim family. A family, Kim. Family, Kim is. Black, the coffee is. Big, the house is. Big, the house yellow is The yellow house is big.