On the school thing – does one of them want to go away to school? In that case, it might not be such a bad thing. My brother and I were terrible children, fighting all the time (cats and dogs fighting, verbal, physical, at least one trip to the ER), and my parents played on our different interests to get us into different schools (not boarding schools, however). We both wanted to go to the schools we attended. He stayed in Catholic school, mostly for the sports program, and I opted for the public high school, mostly for the drama and arts clubs. Of course, my parents made sure the academics were fine in both schools. I’m not sure what they would have done if we had wanted to go to the same school, but they were pretty sneaky in encouraging us on the two schools without making it seem like it was some sort of punishment. Once we were established in two schools, simply having different schedules, activities, and friends removed a lot of the potential for conflicts.
Oh, the activities. A lot of our conflicts resulted from one of us being forced into an activity where the other really shined. I have a lot of sympathy for my parents on this one, it’s bad enough taking kids to one afterschool activity, let alone two. I cried my way through sports camp, he still talks about the trauma he experienced in taking piano lessons even though it was clear he had no musical abilities at all. As we got older, and became able to get ourselves to and from activities without depending mom and dad to drive us around, the emotional relief was palpable. This is something that my parents say they would have done differently – letting us opt in or opt out of things earlier based on our interests and abilities instead of pairing us up because it was more convenient for the car pool.
Heh, my mom just called while I was typing, so I mentioned this to her, and she pointed out that the only thing we continued to HAVE to do together was swimming lessons, because it’s important for all kids to know how to swim (despite me crying through the swimming lessons as well). So there’s some advice from my mom. 
We’re one of the happy ending stories, we’re very companionable now, even though we still have very different interests and lifestyles. We don’t live in the same area, but we talk on the phone and email all the time (we’re in our 30s now). The worst thing we do is pretend to bicker at family events to get our parents riled up, then we bust out laughing. Yeah, we’re not real mature.