In this passage we have the collective singular noun household. Although household occurs elsewhere in the Book of Mormon, this is the only place where it occurs as a subject requiring verb agreement. The 1840 edition replaced the original plural were with the singular was. This change could be the result of intentional editing on Joseph Smith’s part. In accord with the reading in 𝓟, the 1908 RLDS edition restored the original were to the RLDS text. For a similar case, consider Mosiah 23:25, where the original text read “behold an army of the Lamanites were in the borders of the land”. As discussed under that passage, the Book of Mormon sometimes treats the collective noun army as a singular, other times as a plural. Also see the general discussion under subjectverb agreement in volume 3.
In current English, American speakers favor singular verb agreement with groups that can act as a unit (“the committee was”, “the team was”, “the United States is”, and “the family is”). British speakers, on the other hand, favor the plural (“the committee were”, “the team were”, “the United States are”, and “the family are”). Merriam Webster’s Dictionary of English Usage (under collective nouns) indicates that in American English the singular verb is more common for family, but the plural is “not at all rare”, including this 1925 example from F. Scott Fitzgerald: “His family were enormously wealthy”. The evidence suggests that American speakers would naturally choose the singular in Alma 22:23 but still the plural is quite understandable.
Summary: Maintain in Alma 22:23 the original plural were for the collective noun household; as with the word army, either the singular or the plural interpretation for household is possible.