Sounds a bit like my experience at school - I used to fight with another girl at school - we had a love hate relationship, though mostly hate. It went on when we were 7/8 then stopped after that.
She would start being all friendly and nice and then wanted to sit next to me...always just so she could copy my work, which I hated as I thought I might get in trouble for it...you know if we both made the same mistakes then there would be questions as to who copied whom. Sometimes I'd feel a bit sorry for her as no-one else wanted her to sit next to them. We would start arguing about the copying work, then she'd come up to me in the playground and kick me hard in the shins, and I'd punch her on the arm...then usually she'd cry and run off to a dinner lady...who would usually take my side TBH.
She started going to my dance class and I'd already been going for a couple of years already so obviously I was a bit ahead in medals/exams and stuff. I was also very ahead for my age at school.
I honestly now think her mum triggered it off by saying something to her daughter at home, I always found her a bit moody and snappy and wonder if she just couldn't bear that I was on a different reading scheme and so on. Oh when I was seven we did the Nutcracker as a school play and I was chosen as Clara, which probably didn't help - I tended to get good parts as I could remember all my lines and everyone elses. 
Anyway after one fight her mum must have had a word with the school and said I was "Bullying" her daughter and a letter was sent home to my parents. I told them everything that had been happening (had told them bits before)and they spoke to the school, don't recall what they did but it did seem we didn't sit together in lessons as much after that!
Oh, I should also say her mum bawled my dad out at the dance class...now my dad can be stern and a grumpy sod but is also very very patient and mild-mannered, in 35 years I can count on one hand the times he has raised his voice or uttered a swear word...I didn't hear the argument at the time but apparently he did yell at her back and said a few choice words were said
.
Anyway sorry to be long-winded - seem to be getting a lot off my chest recently. My point was we certainly weren't punished at school - and I think what happened to OP's DD was totally unreasonable.