Could someone tell me about good books about Hawaiian mythology?
I've been really interested in it for a long time but I have no idea where to ask for advice or whom to believe.
As mentions by @bleh in a comment, Hawaiian Mythology by Martha Warren Beckwith (1940) seems like a good start.
In the references section of this book you will find a large amount of books/scholarly articles on polynesian and hawaiian mythology. Among the hawaiian references, some names of scholars pop up frequently: those of Joseph S. Emerson and Nathaniel B. Emerson (sons of a missionary), but also Mary Kawena Pukui and Laura Green.
The page on the website sacred-texts.com on Pacific mythologies contains also several other works, in addition to 'Hawaiian Mythology', by Martha W. Beckwith and by W. D. Westervelt.
The works of these few scholars should already cover a significant portion of the subject, I think.