I'm not a psychologist, of course–but someone who angrily explodes every time he doesn't get his way needs to face what he's doing and take steps to overcome it. In extreme cases, they may even need professional help to discover why they harbor so much pent-up anger.
Why is it important to deal with our anger? One reason is because almost nothing is as destructive as uncontrolled anger. Not only does it damage our relationships with others (as you've discovered) but it also leaves emotional and spiritual scars on our own minds and souls. The Bible rightly says that "Anger is cruel and fury overwhelming" (Proverbs 27:4). It also says, "A fool gives full vent to his anger, but a wise man keeps himself under control" (Proverbs 29:11).
The Bible labels unjustified anger as sin, and calls on us to repent of it and seek God's help to overcome it. Often, however, an angry person refuses to face this and blames others for his outbursts–but God's Word is clear: "Get rid of all bitterness, rage and anger" (Ephesians 4:31).
Pray for your cousin, and ask God to give you wisdom in knowing how to help him. His anger is wrong–but God's Spirit can change him. The Bible says, "The fruit of the Spirit is love, joy, peace, patience ... and self-control" (Galatians 5:22-23).