Here Hyrum Smith, while copying from 𝓞 into 𝓟, skipped from the first neither to the second one, with help from the virtual identity of “the kingdom upon him” with “upon him the kingdom” (they differ only in word order). The omitted clause was supplied by Oliver Cowdery when he later proofed 𝓟 against 𝓞. The additional clause is not necessary, although it does fit better with the following reference to all the sons of Mosiah being unwilling to accept the kingship. There would have been no motivation for Oliver to have consciously emended the text here, so 𝓞 undoubtedly had the clause “neither would Aaron take upon him the kingdom”.
Summary: Maintain in Mosiah 29:3 the corrected reading in 𝓟 with the clause “neither would Aaron take upon him the kingdom”.