Hawaii isn't integrated into the United states, instead the US sends aid in the form of industrial and military goods to the small island nation. Hawaii builds large cities and a series bridges from each and every island. Hawaii improves itself threw its ambitious trade and its study of European technology and adapting it. Hawaii decides it needs to expand, and with the help of the United states invades the all the Polynesian islands.
To prevent tensions between the Hawaiian government and the other Polynesian peoples Hawaii proclaims itself a Federation. It would be exactly that, a Federation. The President of the Federation would also be the Monarch of Hawaii and the Chancellor would elected from a group of chosen individuals from every people group.