The only way "Mysterious Island" relates to "20,000 Leagues" is in the ending where Nemo reveals himself to the castaways. In the end, the island, Nemo and the Nautilus (which is trapped in a grotto) are destroyed. The castaways survive. In the novel, Captain Nemo reveals his true identity - which in my opinion, does not match up with that of the novel. Verne had Nemo being from India only after a drawn out debate with his publisher. Verne originally wanted Nemo to be a Polish man whose wife had been raped and tortured and his children sent off to Siberia. Having Nemo as a European fits the clues in the novel much more than that of Nemo being a Hindu.
If you wish to read the novel, it can be found online.
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