Teenage girls can be an absolute nightmare.
There is a massive amount of peer pressure and group-building to try and counteract the massive insecurities that all girls feel, coupled with a fear or not 'belonging'.
Sadly a lot of insecurity is buried under diversionary tactics - if someone else is being bullied and excluded, it's not you.
There is an argument that this is how girls act at this age, but when it reaches the stage where one is being singled out, then that is beyond acceptable. The other girl's mother would be less sanguine if it was here daughter on the end of the exclusion tactics I am sure.
You grand-daughter's mum is doing the right thing by bringing in the school - they have vast experience of dealing with this sort of situation, plus they are on site and can monitor what is going on.
She needs to state her case calmly and without apportioning blame, and get the school on side. I am sure they will reach a resolution without the need to move schools.
Adolescence is more horrible now than it has ever been - fingers crossed your GD gets the support she needs, and with the obvious love and support of her family, she will come through this temporary unpleasantness.