Chapter 17 begins a curious echo of the Sermon at the Temple. The infirm and the children are brought forward (the poor in spirit, etc.). Jesus conducts a group prayer (might these have been the words?). Then we get a perfect vignette or summary of the Worship of the Shalems: the heavens open, angels descend in glory ("fire"), and they minister to the children by encircling them. In particular, we know from 2 Nephi that "encircling" is an image of being clothed in heavenly garments.
I don't know why we have the apparent doubling. Curiously, double visions are a characteristic of apocalyptic literature: the visionary has one vision, and then a second vision to explain the first. This is exactly what we're given in 1 Nephi (8 and 11-14), and I wonder if we have the same phenomenon here.