Oh bless, I had this through my whole school life, secondary School was actually worse, but because I realised that it wasn't going to change, however hard I tried to fit in, I stopped bothering and just pleased myself.
I found 2 girls who where quite and studious but but had a sence of humour, so I knocked about with them for 3 years, they wheren't interested in Class politics as both came from very strict families who didn't allow them to go out without older brothers in tow.
We all ended up at collage together on the same course, and 1 of them her Gran relaxed a bit and allowed her out on a Sat after Church, so we could go shopping together. we all lost contact in about their 2nd year of Uni, but they have a place in my heart still.
BUT! because I had just given up on "fitting in" at School at college, suddenly I was Miss popular, I was known for my quirky humour and don't give a crap attitute to students who thought they where something special, but still polite to people.
I became Clubs and Soc officer at 16 after I had been asked by the president and Socal sec to stand, and this was at a join SU both a UNi and College Shares the SU.
I am much more confident than other people because I carry with me, what is the worst that can happen? they can ignore me? BIG DEAL! I don't get caught up in petty politics becasue I was able to observe it from the outside at school and realise that actually it was worse to be in a clique due to the hurt they could inflict on each other over really stupid reasons, and feel they where pathetic when they made up.
I really geniuning like most people, can empathise (I hope), I don't care if you are a cleaner or CEO if you invite me to the Pub I will come, if I like you which I probably will, unless you are an arse to others...Oh! and no the pub is not the deciding factor 
What my Mum and Dad did for me, like you I bet they where upset, they both talked to the School, I am sure, dispite my pleas not too, I would for my Dts.
they let me know how proud of me they where, they encouraged me to me, if they don't like you when you don't fit in, don't bother it is easier in the long run, encouraged outside activities, spoke to the 2 friends I did have mothers to see if they could relax their rules on their daughters, so they could come to my house or out, this unfortuanlty wasn't an option, but a comprimise was made, 1 friend her adult sister was a chaperone in her house (so I couldn't be alone with any of her brothers) and the other her Gran stayed in the room, we still had fun and larked about.
Your Daughter sound lovely, as you do, big hug's to you both, but as the saying goes what don't kill you...takes a lot to upset me now.