Definitely echoes of "The Cruel Mother". It looks to me as if there "The Wife of Usher's Well" has influenced it too (the idea that the bairns are being called back to where they now belong). Rather than being a creature, it seems to me that the "shape which seemed to her as a rainbow mang the rain" is to be understood as a sign of the Divine Presence before which the bairns intercede for their mother. The rainbow in the rain can surely only represent something good, even if it is frightening for the mother because of her sinfulness. Presumably the "sweet low voice" comes from the same source. I'm not sure what to make of the ending. The bairns' intense pleading seems to invite us to imagine that the mother will be allowed "in" (presumably to Heaven) and washed clean of her sin, but we have previously been told that "they pled and pled in vain", so perhaps not.   

The book where the poem first appeared, Allan Cunningham's "The Songs of Scotland Ancient and Modern", vol. 2 is online at https://archive.org/details/songsofscotlanda02cunn . The song is on pages 70-71, followed by Cunningham's note:

"I have ventured to arrange and eke out these old and remarkable verses, but I have no right to claim any more merit from their appearance than what arises from inducing the stream of the story to glide more smoothly away. It is seldom, indeed, that song has chosen so singular a theme, but the superstition it involves is current in Scotland."

Unfortunately, laying aside the rather unconvincing disclaimer of authorship, that doesn't add much information. What precisely is the "superstition" that he is referring to? That dead children intercede for their sinful parents? That the rainbow can be a sign of the presence of God?... ("Current in Scotland" also looks suspiciously vague compared with the notes to some of the others songs in the book, where he identifies particular localities or even says who he first heard the song from.)