I'm always saddened when I hear parents say that their kids don't like each other. I'm not bragging (well, not much), but our four kids all get along great and always have. I don't say that to be self-righteous. I don't know exactly why our family has so little sibling rivalry. We may just be lucky. If it had anything to do with our parenting, here's what we did.
* Put family first. We enjoyed friend relationships, but we never made them priority over kids. One mom's night out, my husband was at work. Our oldest daughter was going to babysit. Then the weather turned nasty; I called my friend to let her know I wouldn't be coming. She was surprised and actually questioned why I didn't trust my 13-year-old with three siblings in a storm. It wasn't about trust. It was about me being there in case of emergency. Perhaps I was overprotective but the kids felt safer. Attachment parenting meant less socializing, but I don't regret it. It's come back to reward us having happy well-adjusted kids.
* Strive for variable balance. As parents, we can try too hard to be "fair." If I bought something for one child, I didn't always buy something for the others just to even it out. This breeds selfishness. I gave each child what they needed when they needed it. In the long run, everyone should get an equal share of resources. My kids learned to trust that they didn't need to compete with each other for time, stuff, attention or affection.
* Avoid compensation. I had a friend who rewarded her children for going to sibling activities (game, practice, dance class). Kids shouldn't be rewarded for participating in basic family functions. They should be expected to be there for each other. Each family member should get equal opportunities and one child's activities shouldn't always take precedence. But sometimes they temporarily will (like during a sports season). But then it will be another child's turn. Kids understand and accept this. They only get selfish when we teach them to.
* Discuss. I explained my decisions to my kids. If I needed to spend extra time with one child, I told the others why. We talked openly about things. I involved the kids and encouraged them to support each other. I appealed to their innate generosity and compassion and they never let me down. When one daughter was hospitalized for an eating disorder, we had to undergo many therapy sessions with her in another city. It meant lots of travel and we brought all the kids. They never resented it and were actually hurt if I suggested that they stay home. They loved their sister and wanted to help. It turned out to be a good learning experience for all of us.
I don't promise that these tips will proof your family against sibling rivalry, but they worked for us.