Children will never get along with each other all the time. Yet, respect can be kept even within conflict. There will always be fights and sibling rivalry, but it can help relationships to grow if done respectfully. Do unto others as you would have them do unto you. That's the golden rule, and you should explain it simply to children as "Treat others how you want to be treated." A child may not laugh if the joke is on him, and this can teach empathy.
Be a positive role model. "Do as I say and not as I do" doesn't work very efficiently with children. If your children see you disrespecting other people, they will only do the same. If you act disrespectful toward your children, expect the same from them to both you and others.
Role play with your children. Not only are you spending quality time with them, but you can also discuss what is right and wrong. Sit next to your children and pretend to do what your children do to each other. Put each child in the other's shoes in a normal problematic situation for siblings. Looking at it from another perspective will change behaviors all around. Once you have gotten your point across, explain to your children that they shouldn't treat others like that.
Remain fair when it comes to handing out punishments. Be available to listen to every child involved. Hear every side of the story. If a child believes his classmate, brother or sister is getting special treatment, he will only retaliate and disrespect the other child. If a child feels respected, he will act more respectful to others.
Stop your children when they're having a disagreement. Listen to both sides without any interruptions. Have a discussion so that each child can listen to the others. Try to understand his point of view. One child may not have realized what they did hurt the others feelings. Looking back at the situation can help reflect on feelings and actions to prevent future disrespect.
Be patient with your children. Reward them with praise if they do something nice to their classmate, brother or sister. Positive reinforcement works very well. Your child will soon learn that when he is nice and respectful they get the attention they want from you.