If you have more than one child living in your home you are bound to hear bickering. For some families it is pretty constant and for others it is more occasional. Much of this is determined by the ages of the children and the family's argument style. Yes even this behavior is something your kids pick up on. If you and your partner bicker constantly as a way to solve problems then odds are that your kids are going to employ that as a primary problem solving tool. The question most parents have when their kids are fighting is how and if they should get involved.
The answer may vary from case to case but in general it is a good idea to let your kids try to work it out on their own especially when it is a simple disagreement. "It's my turn now" or "that's not fair" or "I'm telling" are all things you may overhear that will inspire you to intervene when the best option may be to just stand back at a safe distance. You'll want to monitor the fight if it begins to escalate into name calling or physical aggression. In those cases you should intervene and let your children know that those behaviors won't be tolerated. Tell them that it is okay to disagree but that they will need to find a more civilized way of working it out. For younger kids you may say a "quieter" or "nicer" way of working it out. If the fights occur in the car, which they often do, the kids need to be directed to keep their voices down because it is unsafe for you to be driving with all the noise. If they don't respond to this, then look for a safe opportunity to pull over to the side of the road and let your kids know that you're not driving under these conditions. Children typically do not like to miss out on things. Whatever it is that you are shuttling them to, whether it is a fun activity, a class or a game, can wait until it is safe to continue. If you do pull the car over, they will most likely take you seriously when you give them the initial directive the next time.
Kids need to learn these problem solving skills and for better or worse we all first learn these behaviors at home. If you notice your children engage in constant scuffles that don't seem to end well or at all, you may need to sit them down during a quiet moment and give them some conflict resolution tools. Teach them how to allow the other person to state their opinion (you can even use a timer that gives each child 2 minutes to say what is upsetting them). Let them know that no one can hear them when they are yelling and that they will never get their point across simply by saying it louder. Give them words such as, "how can we work this out together?" or "what do you think would be a fair compromise?" Teach them that compromise really means that everyone is a little bit happy and a little bit unhappy.
You can't avoid these conflicts altogether and you wouldn't want to because, as I mentioned, it is how we learn. You can be aware of situations that set your kids up for a battle though and it is wise to avoid those. Try to be as equitable as possible as a parent, but remember that each child is an individual and in life everything is not always equal. Be clear about the family rules, such as privileges granted to an older child. This means that everyone in the family is aware that those privileges are reserved for when you are a certain age and that is not negotiable. It may not seem fair to the younger child but you can remind them that they too will one day be the golden age to receive that privilege.
When you see that the argument is manageable (no name calling or aggression) you may even ask your kids to take it in another room. Often kids quarrel to get your attention and in the absence of an audience what they were fighting about no longer seems so important. Alternatively, you can walk out of the room and remove yourself from the feuding. And as always, pay attention to how often you are engaging in arguments with your mate or out in the world. Role modeling is the best teaching tool we as parents have at our disposal.