In his editing of 𝓟 for the 1837 edition, Joseph Smith replaced the singular doth with the plural do twice here in this verse. In both instances the subject is plural; thus he edited the text to “children do have” and “words ... do confound”. But the 1837 edition itself followed only the first of Joseph’s grammatical emendations in 𝓟. In the second case, the 1837 edition dropped the do, perhaps accidentally. There seems to be little grammatical motivation for dropping the second do auxiliary in the 1837 edition while leaving the first one, especially since the do auxiliary is sometimes repeatedly used within the same passage (as in the example from Helaman 6:3 cited below).
The original text of the Book of Mormon freely allowed plural subjects to take verb forms with the -(e)th inflectional ending (which was historically the third person singular ending). For discussion of this point, see the phrase “Nephi’s brethren rebelleth against him” in the 1 Nephi preface. In modern English, the nonemphatic uses of do have and do confound sound awkward. It is actually easier to accept doth in these two cases because the archaic doth is biblical sounding, but do is not; we are therefore more inclined to accept “children doth have” and “words ... doth confound” than “children do have” and “words ... do confound”. For another example of the editing of doth to do in the text, see under 2 Nephi 4:18 (also see the more general discussion under infl al endings in volume 3).
Elsewhere in the text, there is one instance of do have, namely in Alma 9:23: “contrary to the light and knowledge which they do have”. There are also 16 instances in the text of the past-tense did have, including one that shows multiple use of the do auxiliary (as originally in Alma 32:23):
There are also seven other instances of the do auxiliary used directly with the verb confound, as in Alma 37:7: “and by very small means the Lord doth confound the wise”. The critical text will, of course, restore both instances of doth in Alma 32:23. For further discussion of this usage, see under 1 Nephi 2:14 (or, more generally, under do auxiliary in volume 3).
Summary: Restore in Alma 32:23 the two original instances of doth: “little children doth have words given unto them many times which doth confound the wise and the learned”; the Book of Mormon text allows verb forms with the inflectional ending -(e)th to occur with plural subjects.