Yikes. LW is disturbingly and off-puttingly invested in her daughter's social life and she needs to find some boundaries, fast.

Lizzie is getting along fine with the kids at school who don't know her mother, and she was getting along with the neighbor kids until LW's overreaction to the situation with Grace's mother. I would bet a shiny nickel that Lizzie's exclusion in the old neighborhood was probably at least as much LW's fault as well.