I've raised four girls, and I hope that I can offer some suggestions.
First of all, have Mom of grandaughter read the book "Queen B and the wanna B's", a great book about the behavior of girls, and especially the social hierarchy of "tween" girls.
Most local churches have a youth group, and most consist of well rounded, nice girls. Usually the youth pastors do not even care if you are a different denomination of the church they are pastoring. Their goal is to provide a safe social environment for kids, and most DO.
Four H and Girl Scouting are also great places to meet and mix with other, wonderful families.
We showed rabbits, the Holland Lop variety. It's fairly inexpensive and it introduced all three of my girls to some very wonderful people.
Last, try to stress to your grandaughter that middle school/high school are really a small part of life, and everybody changes when they grow and mature...
Don't understimate the power of home schooling if things get too rough. It just might save her life, and there are great home schooling groups that meet regularly to socialize.
LOVE, LOVE, LOVE her and find her some outside interests, and tell her that there are wonderful people in the world praying for her safety and hurting for her from afar.
Tell her this for me... You'll make it, Baby, and you'll be a much stronger, better person than all those girls that tried to break you down. You can do it. Be strong and remember, you are NOT alone.