Civility happens on the edges of self-management. It is the very nature of a child not to have learned self-management yet. That is what a child is. Maturity is all about growing a self-possession. A child begins as a narcissist and only works into a social worker over time! Self-management is difficult, even for adults. As the late Margaret Thatcher (former Prime Minister of England) said, "civilization is a thin veneer." Up the pressures a notch higher, enlarge the gulf between perspectives, up the "toys", and you have full-blown war.
Maturity means being able to suspend one's own perspectives long enough to see issues from the other person's point of view. This adroitness extends to being able to even get into the feelings of others, too. Social development is a process of recalibrating responses, after having become fully aware of "otherness".
So, when one has a houseful of young undeveloped perspectives, how does one parent successfully ride these dynamics? The wise parent hastens the outcomes by cultivating in the child the strategy of going the extra mile. By repeatedly stretching the limits of what the child is required to do socially, a normal social development will occur naturally and progressively. "Let's see how we can make your brother feel extra special and work him out of his disgruntlement!" "What can we do extra to give your sister a joy she hadn't counted on?"
The parent then concludes every challenge by drawing attention to the results accrued to the "giving" child's own soul. "If you make your sister feel good, you will feel good!" One can even bait the child on the front end with that comment. "Want to feel good? Go relieve your brother of some burden; give him something; help him." The act of going beyond is the bunker-buster of self. The principle is: "Not only are you kind to your neighbor, but once in a while you water your neighbor's garden." This releases the sweet perfume of social harmony. Relationships were originally designed to bring us untold joy, rather than just exist on the plane of endurance. It's a tough swim upstream to discover that, but the sweating parent's faithful coaching will bring it about.
You can begin this process with the word "Let's." You do it with the child to the other child, or other parent. "Let's go rub your dad's feet. I'll do one, you do the other. Let's make him very happy." You inspire by giving the child an idea he would have never thought of on his own, and then you go do it together. He then feels the joy accrued to his own soul via the new challenge of going totally beyond himself. Gradually you wean the child off from having to do it with him, until he is doing these sorts of things by himself and loving the feeling he gets while doing it! When he is achieving his own emotional rewards, he won't need you anymore.
By the way, this principle of doing it with your child governs all of your parenting over that child’s challenges. If your children are having trouble with academics, chores, business building, etc., you begin by doing it with them, and then subtly backing out incrementally as they discover their own capabilities.