One wonders here if the preposition in might have been accidentally added to the text during its dictation. 𝓞 is extant here and reads “the cause in which they had undertaken”. Elsewhere the verb undertake takes only a direct object as its complement, not a prepositional phrase headed by in:
When taking down Joseph Smith’s dictation for Alma 46:29, Oliver Cowdery first thought that the direct object for the verb undertake was an infinitive clause; Oliver initially wrote the infinitival to after undertaken, but then he erased the to and wrote therefore. This error may have distracted him from realizing that he had incorrectly written the preposition in at the beginning of the relative clause.
An extra in could have entered the text here as a result of familiarity with the expression “the cause in which they had engaged”, common enough in American English during the second half of the 1700s and the first half of the 1800s, especially when writing about the American War for Independence. A famous instance of this usage is found in the general orders of George Washington at Gulph Mills, Pennsylvania, on 17 December 1777, prior to entering winter quarters at Valley Forge: “and the sacred cause in which they are engaged”. Many of the examples listed on Literature Online are in the perfect active, as in the following citations where the verb is engage (here I regularize the spelling and ignore other accidentals):
An alternative form of this expression that could have influenced the text in Alma 46:29 is “the cause in which they had embarked”. This expression was common in the first half of the 19th century; Literature Online has the following citations where the verb embark is in the perfect active (once more I regularize the spellings and ignore other accidentals):
It is doubtful that the original text for Alma 46:29 actually read engaged or embarked instead of undertaken, especially since neither of these words otherwise occur in the Book of Mormon text. The more reasonable assumption is that the original verb phrase was “had undertaken” and that the in was accidentally added during the dictation of the text (by either Joseph Smith in his dictation or Oliver Cowdery as he wrote down the text). The reading in Alma 46:29 with the preposition in seems quite incorrect, so the critical text will assume that the in is secondary.
Summary: Remove in Alma 46:29 the in that heads the relative clause “which they had undertaken”, thus emending the verse to read “the cause which they had undertaken”; the in was apparently inserted because of familiarity with two common expressions of the time, “the cause in which they had engaged” and “the cause in which they had embarked”.