The original manuscript is extant here and reads “and the resurrection of the dead bringeth back men into the presence of God”. When Oliver Cowdery copied the text into 𝓟, he accidentally wrote bringing instead of bringeth. The correct reading was restored in the 1830 edition, perhaps because bringing didn’t work very well and in the preceding clause the verb was bringeth (“and the atonement bringeth to pass the resurrection of the dead”). Another possibility is that the correction was made when the 1830 sheet for this passage (the 22nd signature) was proofed against 𝓞. For the evidence of this possibility, see the discussion under Alma 42:31.
Summary: Maintain the original two occurrences of bringeth in Alma 42:23, not the bringing in 𝓟 for the second occurrence of the verb bring in the verse.