In what ways does R. M. Ballantyne’s The Coral Island, chapters 19, 20, and 34, support the belief in British imperial dominance, specifically in relation to race, culture, and morality?

Obviously, the three main characters in this story—Jack, Peterkin and Ralph—are white boys. In chapter 20, the text shows us their natural adaptability and ingenuity as they work to make themselves outfits from coconut cloth and make the home they have built for themselves more habitable. They even come to learn how to swim "like fish" and to catch fish to eat. All in all, the boys are represented as capable and clever, able to maintain a civilization even under these circumstances.
By contrast, when we are first introduced to the native islanders, they are described as "fierce cannibals." When the natives disembark, they are naked, carrying spears and clubs. The scene of battle between the two groups of natives is described as "frightful," the men "dash[ing] out each other's brains" with their clubs. The chief of the attacking party, moreover, is described in extremely dehumanizing language: he is tattooed all over and has "white teeth" like a "terrible monster" made only for killing. Throughout the narrative, the "blacks" are described in terms of their violence, and words like "savages," "monsters," and "creatures" suggest that these people are not human—even before the boys bear witness to active cannibalism. The natives even, in opposition to what the boys consider "civilized," attack women—who, notably, are lighter in color than the "savage" blacks attacking them. There is a strong indication that the darker the skin, the more savage and violent the people.
Notable too is the fact that, at the end of this chapter, we see the white boys outwit the warriors, despite their limited experience and young age. By virtue of their civilized whiteness, they are painted as naturally able to defeat the "savages" at their own game, their "victory" assured.
In the following chapter, we see the boys display their hospitality and begin to teach civilization—and language—to the "savages." The interaction between the groups is paternalistic—again, although the white boys are not even adults, they enforce their own views and culture upon the natives, interrupting an act of cannibalism and berating the man who had been about to eat the flesh of another (although this is, according to the narrative, one of the natives' cultural practices).
In chapter 34, we see the natural end of this attempt to enforce white culture upon the natives: "Tararo has embraced the Christian religion! The people are even now burning their gods of wood!" Here, the native people have been fully converted through the efforts of an English missionary and are now Christians. The boys perceive this as a victory for themselves and for "light" (note the opposition of "light" to "blackness"), and there is little consideration for the existing culture which has been overwritten in this way.