I have a 6.5 yo dd who had/has a frenemy like that, too. It made me so annoyed to witness the behavior! Fortunately, we switched schools, which prevented daily contact. But during the relationship a year ago, I would talk to my dd about what qualities were important in friends, and how she wanted her friends to act toward other people, including her. And that I'd ask whether this "friend" had those qualities. (My dd would say, '"Sadly, she doesn't." ) We also talked about what friends "don't " do, which I hoped would also plant a seed for my dd. This little girl also misbehaved at our house during playdates and would throw crazy tantrums when it was time to leave. That, too, was a good opportunity to talk about what kind of person my dd wanted to be and to be friends with.
Hopefully that helps!
