That also sounds very similar to me and my sister when we were growing up; though we were never specific, as you quoted your girls as being...it was more of a general "I hate you!" kind of atmosphere for about, oh, 5 years. Till I left for college.
As MamaChicken related, my sister, too, is bipolar, but was not diagnosed till after I had left the house. Not that I'm saying that's the problem, esp. since it seems that both girls are "giving and getting" it equally.
The reason it is better for me and my sister now is that we are living individual lives 2000 miles apart. I know you only have the girls for the summer, but is there a chance for them to be apart from each other at least a few days a week? Friends to hang out with? I think middle school is such a tough age to be sisters that close in years, because you are both wanting very much to be "individuals" but you are lost without each other, too. Do they at least have separate bedrooms at your house: a place where each of them can go to be by herself? Middle school for me caused a need for some serious, solitary introspection!
I am glad that you have been able to stop the physical mean-ness, but yes: my sister and I would have verbal screeching matches that would put my mother in tears.
And oooh: we were (are?) so competitive!!! It was ridiculous; still is. Would family counseling be an option for you all this summer? My parents started that with my sister after I had left for college, and I'm not sure how much it helped her, but it really helped my parents to deal with my sister's moods and actions in a much more final and positive way.
I wish I could help more...but I must admit that I am not much good for this, because my sister and I still have so many, many problems. I dearly wish that we all would have gone to counseling as a family, or even just sent me and my sister for sibling counseling! I think it would have helped a lot.