There really is no point to it, they have zero standing for custody. And they really have zero standing for even having contact or phone calls. But, I agree, Lori did it for control. She could, so she did.
That still doesn't explain Tylee's disappearance.
But, after hearing what a great Mother Lori was, it fits with narcissism. She was a good Mother, for herself, so other people would say how awesome she was. The child is an extension of her, so if the child has any flaws, isn't pretty enough, smart enough, whatever, it is useless to the narcissistic. Useless.