Sounds similar to our house as well. Our oldest, 12 and almost 11, are best friends and usually get along wonderfully ... but when they bug each other they BUG each other! :lol: Our "middle child" is almost 9 and having older brothers and a 5 year old younger brother, I think she feels left out a lot because the older boys see her as too young and she's too much older than the younger kids. However, she gets along with kids of all ages and likes to hang out with adults as well as spend time alone in her room reading. Our youngest two are 5 (boy) and 3 (girl) and they get along great. Our 3 year old's best 3 year old friend is at our house 4 days a week (I provide childcare for her) and we also have a 1 year old "borrowed" little girl 3-5 days a week.
We're basically an unschooling family. We have "homeschool hangout" on Wednesdays where I teach the olders things based (somewhat loosely and very creatively) on the Picturing America posters and my friend teaches the littles (story/craft) and in the Fall, Winter and Spring we are members of a homeschool co-op that meets from 9:30am-3pm (5 1-hour classes) and the kids love the variety of classes they can take there (and I teach a class for 3-5 year olds). Things tend to work well in our family. The kids work on things they're interested in, and because they're excited about what they're learning, they share what they learn with the others, so we all end up learning a lot without much effort. ;) A couple of my kids prefer to read about things, a couple like to learn by doing. It's actually a really good balance for doing projects with partners or in groups.
As far as keeping the household harmonious ... it isn't always, but that's part of life. There are enough spaces in our small house to send people, projects for them to do, books for them to read, that I can encourage them to take a break from each other as needed. We also have a quiet hour almost every day, when we all need to find something quiet to do for about an hour so we can all recharge our batteries (and so I can get the littles down for a nap!).