Regardless of how well we get along with others, the time will come when we disagree. It is just a simple fact of life. The question becomes: the example we set.
The actual act of disagreeing is probably healthy for your children. Think about it this way. children learn from the examples that the adults in their lives set. If the children only ever see the positive aspect, how will they learn to appropriately deal with conflicts? Conflicts in life are a given. What we do with conflict is a choice.
If we want our children to be a leader with compassion, a friend of the friendless, a defender of the weak, an independent thinker and empathy abound, you must exhibited these traits and practice the art of fighting fairly.
When a disagreement is arising, make a mental decision to fight fairly. Show your children that there are peaceful and loving ways to resolve differences of opinions. Listen to what the other person is saying, repeat back what you heard, maintain a calm voice, never use foul language or call each other names and ALWAYS stay respectful.
At the end of the quarrel, if both parties stayed courteous, compromised, and found a peaceful resolution, the children just learned an extremely valuable lesson.
We want our children to sometimes shake things off. At other times we want them to take up a cause. Yet we also want them to be willing to compromise. But, the main thing we want is for the children to distinguish which situation requires which action. The only way young minds can sort through the rubble and be able to quickly determine a path is to have been a witness to or a party of conflict.
Of all of the lessons we are charged with, conflict resolution skills is of top priority. While our children are young, we have their hearts, minds and attention primarily focused on us. We are their primary source of role modeling. Whatever you do, don't go behind those closed doors to fight it out (unless you are going to set a negative example.) Show the children how to fight fairly. That lesson will follow them for the rest of their lives.