Do not invite her to any other social events, she will get the message.
I am glad the little girls parents are working with everyone and admit their daughter has a problem though, DS1 was bullied by a child in school that had been thrown out of 3 pre schools and his parents never admitted he was a problem, even now this boy is in high school his parents still insist he never does anything, shocking bad parents imo.
I am sure with support this little girl will do just fine, this nasty mother is going to have a bloody shock when she gets to the real world of school.