I have 3 kids, and I've seen what you're talking about. For years, I despaired. The oldest, a girl age 14 now, is the "mean" one. The others, boy-girl twins, are age 12.
The girls, esp the older one, wanted to leave my son out. He did annoy them, but he's a boy, so that's the way they are w/ sisters. I talked to him, explaining that girls don't like to be teased all the time, etc, etc, but of course things pretty much didn't change at all. He has low self-esteem issues, too.
Likewise I talked to the girls, don't leave him out, etc.
When the oldest dd isn't here, the twins get along fine.
We homeschool, so they're together all day. When ds12 is with other kids, he's great. No self-esteem issues at all. I've been trying to get him together more often with friends, cousins, and recently his uncle has come to shoot guns w/ my husband and ds12, or ask ds12 over to shoot at his house.
I used to try to find activities that separated them, so there would be no fighting. This didn't fix the real problem however.
One thing that has seemed to help, is that *I* do something with *all* the kids. They would rarely play together otherwise. We play games, walk, play the Wii (I take turns being on each kids' team), and we read together, esp the twins and me. They see how I react if I lose, which on the Wii is nearly every time! =D We've played charades, and other games of that sort. I've tried to spend time w/ each kid, just letting them talk. This is mostly around bedtime.
The second thing I'm doing, is when they do fight, I try to talk to them and ask them how they think the other person *felt*. Does Jesus want us to make others feel that way? (Yes, but he did this... she said that...) How does Jesus want us to act toward others who aren't kind? How can WE be more kind?)
Now they are beginning to get along better, and do some things together.
Just recently, dd14 commented that ds12 is starting to grow up. I've watched for ways to comment him on that, if I see any sign of maturity. Plus he's taller than I am now, and catching his twin. He really likes that!
Dd14 has shown signs of being more tolerant of him also. We've been reading our Bibles more, and most nights if I go *back* into her room after saying goodnight, I'll see her reading her Bible. =)
I know your kids are quite a bit younger, but this is my experience, and maybe will give you some ideas. Maybe it won't take as long as I did to figure it out! =\