Along the lines of the previous post about a young child who is pitching a fit, a friend who raised six children gave the following advice:
The parents trained the child to scream by giving him what he wanted when he did scream. Now they need to retrain what they trained into him by not giving him what he wants – whether he screams or not. They must be gracious and kind, but firm. Their faces don't need a smile, but the eyebrows should be a little raised, with bigger eyes, and not squinted. There should be no furrow or frown, but a pleasant look of finality. The parent may even need to hold the child firmly, but never respond harshly or with unkindness.
Let the child scream, and if need be, move to a closet so neighbors do not hear. Wear ear plugs if needed, but do not give into the child’s tantrum. No child will scream forever. He will wear out, and if you have been loving, you will win at last. At the same time, try to find a pleasant diversion for the child that would move him away from the screaming. You might take him into the kitchen to get a drink for yourself, and ask if he wants one. Or give him a nice piece of banana to draw his attention away from his screaming, and from what he wants that he is not getting. You can go about your work, but don't purposefully punish him by removing your presence. Your misbehaving child needs the security of your love and presence for this to work quickly.
The older sibling, the one who has been modeling the selfish behavior, needs the same treatment. If at all possible, the two children should be removed from one other when one or both are screaming (because the one’s screaming incites screaming in the other). (Usually this will require two mature adults, perhaps another mother or a trusted friend who can help with this retraining for a few days, in expectation of a quicker turnaround.) Screaming makes everyone feel uptight. Soft calming music such as hymns or light classical can be played to relieve tension and uplift the spirit.