The question in this passage is whether “O house of Israel” should be attached to the preceding people (as in the LDS text) or to the following clause (as in the RLDS text). The 1830 typesetter punctuated this passage so that the latter held: he placed a period after people and a comma after Israel. For the 1849 edition, Orson Pratt reversed the punctuation, placing a comma after people and a period after Israel.
The reading in the LDS text is very probably the correct reading. Elsewhere in the text, we have 12 occurrences of “O house of Israel” where each is connected to a preceding occurrence of people. In nearly all of those cases, the following clause begins with a connective word that does not permit a preceding vocative like “O house of Israel”. In eight cases, the connective is and, just as here in 3 Nephi 20:12–13. Other connectives are that, verily, and therefore (each occurring once). In only one case do we get a situation where the following clause doesn’t have a connective, which would then allow “O house of Israel” to be attached to that clause, at least in theory:
Yet even here “O house of Israel” cannot be attached to the following clause beginning with listen since this clause already has a vocative (“O isles”), just as the following clause does (“ye people from far”).
Here in 3 Nephi 20:13, the 1840 edition removed the and of the clause following “O house of Israel”. The original 1830 punctuation implied that “O house of Israel” should be attached to “and then shall the remnants …”; but the and made this rather difficult, so the and was probably deleted for that reason. The evidence thus strongly supports the 1849 interpretation that “O house of Israel” is connected to the preceding people. There is no reason to follow the 1830 punctuation, nor to delete the and at the beginning of verse 13.
Summary: Accept the current punctuation for “O house of Israel” at the end of verse 12 in 3 Nephi 20; this vocative phrase belongs with the preceding people; there is therefore no reason to delete the connective and that begins the following clause (in verse 13).