I'm slowly starting to wonder if mom might have some sort of mental illness. Something along the lines of a psychosis, which makes her believe her child was still at home until she reported her missing (while maybe that same psychosis made her harm her child weeks ago).
I mean, the having the water running in the bathroom, mentioning her daughter to the movers, reporting her missing and being cooperative with police might fit this scenario IMO.
Mental illness might also have to do with a very dirty house and maybe even having to move to a bad place in town.
I don't want to stigmatize mental illness at all, so I hope I don't hurt anyone by suggesting this. It just popped up in my mind as one of many possibilities, especially since psychosis can come in many different forms.