It's unlikely, I should say, that there's any relationship at all between the comic Amphitrite here and the broadside song made on a real shipwreck; though the name of the latter may perhaps have suggested the name of the former. Equally, Rounding the Horn is not related to either, and indeed only one version of it found in tradition even mentions an Amphitrite. I have my own ideas about how that name got into this last song, and what may be a more likely candidate for the ship; but you'll have to wait for that until The Penguin Book of English Folk Songs, re-branded as Classic English Folk Songs, is published by EFDSS (in time for Christmas, we hope).