The expression “their king Mosiah” has been treated in the first two editions and in the LDS textual tradition as if the name Mosiah is in nonrestrictive apposition (namely, by having a comma before Mosiah). However, it is also possible that this construction could be treated like the Hebraistic “the king ” found elsewhere in the Book of Mormon text. As discussed under Mosiah 19:15, there should be no punctuation after the king in such constructions involving names (for a complete list of examples, see under hebraisms in volume 3). The similarity of “their king ” suggests that no punctuation be placed between their king and Mosiah in Mosiah 27:1 (which is how the RLDS text reads). There is one more example of “their king X” later on in the text:
For the same reason, the comma could be dropped between their king and Amalickiah in Alma 49:25.
Summary: Omit the comma after “their king” in Mosiah 27:1 and Alma 49:25 since the construction “their king X” seems to parallel the Hebraistic construction “the king X”, which is occasionally found elsewhere in the original text.