Here the 1874 RLDS edition omitted one of the repeated their ’s; the 1908 RLDS edition restored it. Such repetition of the determiner is characteristic of the Book of Mormon text, as in these examples of multiple conjunction:
For a general discussion of this usage, see under conjunctive repetition in volume 3.
Summary: Maintain the repeated their ’s in 3 Nephi 5:3 (“all their sins and their abominations and their whoredoms”); such usage is characteristic of the Book of Mormon text.