I think it is very important to understand that the mom (much like many other characters in this story) is more than 2 dimensions. At the base level she is a manipulative bitch, but digging deeper would most likely be pain and anger from her husband and his (I assume) infidelity. Thus, she has conflicting emotions when it comes to Koto. While she hates the idea of being left alone by anymore of her family, she likewise hates that Koto reminds her of Koto's father. I doubt the mother believes she is lying when she tells Koto she loves her and does not want her to leave, but she cannot help but act horribly manipulative despite this.
This is in no way saying that what she is doing is okay, as I still believe she is unfit to be raising a child in her current mental state. I forgot who it was, but someone commented something to the effect of "this series will make you think things are getting better before making you depressed every 3 chapters".