R. M. Ballantyne 
Island Queen 

Castaways in a sea of danger! Pauline, Otto, and Dominick were children cast into the wild South Sea’s ocean. The brave Rigonda family of England, however, clung to life on their lifeboat despite the demise of the rest of the castaways, searching weakly for a sail in the distance. Instead, they found a dead ship, wrecked on a reef. And the reef, most fortunately, was by an island. They were castaways, little Robinson Crusoes on an exotic volcanic South Seas Island. (Amazon)