Both manuscripts read without any direct object for the verb knew. The 1830 typesetter added it after knew, perhaps accidentally. Subsequent editions have maintained the it except for the RLDS text since 1908 (the 1908 RLDS edition restored the reading in 𝓟 without the it).
Elsewhere in the text, we have two examples of knew followed by it, but there is one example where knew has no direct object (marked below with an asterisk):
For an example in the manuscripts of the tendency to add the direct object it, see 1 Nephi 1:11, where in 𝓟 Oliver Cowdery’s initial correction to 𝓞 read “and bade him that he should read it”. There Oliver immediately erased the it, which implies that 𝓞 did not have the it (𝓞 is not extant here). There would have been no other motivation for Oliver to remove the it in 1 Nephi 1:11 since that reading is perfectly fine. As another example where an it has been inserted into the text, see under 2 Nephi 17:11; in that case, the 1830 typesetter supplied a direct object it after ask in “ask either in the depths or in the heights above”, probably under the influence of the corresponding King James passage (see under 2 Nephi 17:11 for discussion of this change, which was most likely intentional).
One wonders here in Alma 56:48 if the subordinate conjunction that should not follow the verb doubt (“we do not doubt that our mothers knew”). Unfortunately, there are no other examples in the text of doubt taking a finite clause as its direct object. The original manuscript is extant here in Alma 56:48, and there is no that (inserted or otherwise) after doubt. There is therefore no manuscript evidence for emending the text by inserting a that after doubt in Alma 56:48.
In fact, there is reason to believe that the finite clause “our mothers knew” is not the direct object for the verb doubt but an independent clause. Grant Hardy, in his FARMS publication “Of Punctuation and Parentage”, Insights 24/2 (2004): 2–3, suggests that a semicolon could be placed between these two clauses in the current text: “we do not doubt; our mothers knew it”. He also mentions this punctuation in a footnote as an alternative reading for the passage in The Book of Mormon: A Reader’s Edition (Urbana, Illinois: University of Illinois Press, 2003). The language at the end of the previous verse is supportive of this reanalysis of the punctuation: “yea they had been taught by their mothers that if they did not doubt that God would deliver them” (Alma 56:47).
It is also supported by language in the next chapter:
Hardy’s suggested emendation in punctuation allows one to interpret Alma 56:48, even without the intrusive it, as explaining that these young Ammonites said that they did not doubt and that their mothers knew, namely, that God would deliver them if they did not doubt. In other words, the issue here is not one of doubting whether their mothers knew. The critical text will accept Hardy’s suggested emendation by placing a semicolon between what appears to be two independent clauses, especially in light of the two references elsewhere in Alma 56–57 to these young men’s lack of doubt that God would preserve them.
Summary: In accord with the reading of the manuscripts, remove in Alma 56:48 the pronoun it after “our mothers knew”; there is no evidence for inserting a that after doubt in “we do not doubt our mothers knew”; in fact, references elsewhere in this part of the text argue that the original text here in Alma 56:48 has two independent clauses, “we do not doubt” and “our mothers knew”, which means there is a need for some kind of punctuation break (such as a semicolon) between these two clauses.