Anger is such a difficult emotion to manage, even for adults, let alone for children. It comes from feeling violated, stepped on, overlooked, treated poorly. We are all so frail underneath, that any episode of not being loved is almost too painful to bear—so we lash out. We were all originally created to have a legitimate right to a protected personhood, i.e. being treated with nothing but love. That was God's original design. So anything but that, throws us for a loop. Due to the Fall, we not only have our own crookedness to deal with, but interfacing with others' fallen natures, to boot. We are always surprised and unsettled by other people's unkindness to us, no matter how frequently we experience that, because it is not our expectation, having been made perfect (before the Fall) and in God's image.
So, here's tool # 1: Change our expectations about others.
Expect others to be unkind. Don't be looking for a five-star hotel, when life is really a reformatory. Teach your children that they will experience many episodes with many people—too many to count—over a lifetime. Expect it. Tell them to saddle up / put their seatbelts on. Disillusion them about all people early on :) Teach them that people weren't put on this earth to love US, they are in our life to give us practice in loving them.
Tool # 2: Go for a brisk walk.
There is no emotion that cannot be settled to at least some degree by a long walk. Teach your children to delay dealing with their problems with other people. Train them to seek to settle almost nothing in the heat of the battle. Teach them to withdraw. Unhook. Take deep breaths. Tell your angry child: run to the fence outside, or the mailbox ten times, and then we will deal with this matter, perhaps even after naptime. Patience. Developing the ability to delay anything is maturity. Impetuosity is immaturity, in every case—even in adults.
Tool #3: Spread the matter before God.
Hezekiah, in his utter extremity, taught us how to cope with outlandish provocation from others and do it with success. When Sennacherib threatened Hezekiah with a vile letter (II Kings 19), Hezekiah did not answer Sennacherib. Instead, he went into the Holy Temple and spread out the letter before God. By doing so, he would have never needed to speak to Sennacherib about it, really. His relief in the matter was total. We need not spread the problem out before the other person, if we have spread the problem out before God.
(Now, in a family we can and should eventually work through that episode via some peaceful conflict resolution later to avoid a reoccurrence in an ongoing relationship—but it works best if we do so only after we have spread the matter out before God.) And with extended family, it need never be spoken of or resolved, if given to God.
Stuffing anger doesn't work. Shouting at the other person doesn't work, either, "For the anger of man does not produce the righteousness of God" ([James 1:20; ESV)—ever! So, who do we tell? Tell God about it immediately. Name the sin of the other person. Tell God specifically what they did toward you and how awful it feels, and then ask Him how you should respond cope. Use God as an understanding best friend. Talk to Him, at the moment. He wants this. This will keep your children from developing ulcers!
Tool #4: Meditate on the other person's good points.
A person is always far larger than this one cantankerous moment. Therefore, sometimes get your children to name (aloud) three good qualities of the person who has just offended them. Name those first. (Teach them to do this always mentally—even if it is not spoken). This immediately puts the conflict into perspective. Teach them to mentally reposition the offender in a larger setting. Help them recall that the offender was a sharing person with you yesterday, and that you will rule angels together, tomorrow, and that the "awful offender" (really, just your wee sister, or spouse, or father-in-law) is faithful, hard-working, struggled at birth, has a cold, etc.!!! It has been said: "There is enough in every person to make them out to be a demon or a god, depending upon which you focus upon!"
Tool #5 Memorize all scriptures about anger.
Review them. They're priceless.
Tool #6 Teach children how to fix their anger.
Teach them to get good at doing emotional repair jobs. Most all of us are too immature to do it right even 50% of the time, even if in calm moments we know what is right to do. About 98% of the time, we'll blow it. So fix it; do it right later, even if you've done it wrong at the moment. And release the offender from the offense at their motive level. In other words, believe that they didn't mean to hurt you—they were just after their own "crayon" to finish their project even if it meant roughly wrenching it from your hand. Everyone is "me"-driven. It has been said that "people care more about their own headache than if you die." Make your peace with their frailty and their self-absorption, because, given the right "off" moment, you have it, too.
Anger is the subject of one of our 48 character traits in our coloring book and songs for young children.