Dan Millett was a tribal elder at the Duckwater Shoshone Tribe when I worked there. A couple times he came by my office just to talk. One time he told me a couple Indian legends. I wish I had been able to take notes, or record them as the stories were fascinating. In the case of his version of the "water baby" you could easily see how this would encourage a young mother to take care of her babies.
Being from Duckwater, this has a local slant. The water baby is a kind of spirit creature that inhabits the water, in this case the Duckwater ponds which are formed by the springs. It is the custom in Duckwater to put babies in a cradle board. They cradle board raps them up tight, which is very soothing to babies. However in can lead to a mother being lazy. They might hand the baby in a tree, where the wind will gently rock the baby. However, if left in the tree, the baby may be inhabited by a water baby. This is most likely to happen if the baby is fussy. If a baby is inhabited by the spirit of the water baby, then it will also inhabit the mother while nursing. If this happens the mother becomes a zombie like creature--half alive and half dead.
The legend of the rock family I did not get as well. He talked about a family from the Reese River area. Somehow the family had been turned to stone. He said he had actually seen the stone family. They were gigantic.
I found this blog which talks about both these legends, with a different slant and attributing them to Pyramid Lake area.