Your care for your younger sister is evident and it is right to bring her before the Lord. God hears the prayers of those who love others and desire for them what He Himself desires, which is true peace.
The world often speaks of peace as simply the absence of conflict or the quieting of outward circumstances, but that kind of peace does not last and it does not reach the heart. Real peace begins with being at peace with God. That peace is only possible through Jesus Christ, who made peace through His blood shed on the cross. When a person is justified by faith in Him, the war with God is ended and sins are forgiven. Without that foundation there is no lasting calm inside, only a constant inner turmoil.
Once we have peace with God, He wants us to know the peace of God in daily life, the peace that guards the heart and mind and passes all human understanding. Scripture says God will keep in perfect peace the one whose mind is stayed on Him, because that person trusts in Him. Jesus said to His disciples, Peace I leave with you, my peace I give to you, not as the world gives. That is not a peace that depends on everything going well, but a confidence that God is in control and that He is working even in difficult moments. It comes as we turn our thoughts toward Him and learn to trust Him rather than our own reactions.
Anger is part of what the Bible warns us about. There is an anger that is not sinful, an anger at sin and evil itself, but the anger that controls us, that flares up quickly, that leads to bitterness, wrath, shouting and unkind words, grieves the Holy Spirit. The word says, be angry and do not sin, do not let the sun go down on your anger, and let all bitterness and wrath and anger and clamour and evil speaking be put away. The wisdom that comes from above is peaceable. It leads to peace and it makes peace with others. Those who sow peace reap a harvest of righteousness, and Jesus called peacemakers the children of God.
God does not only want to help us manage our temper, He wants to change our nature. He wants to bring us from being governed by self to being governed by His Spirit. There is a battle within for the control of the mind and life, between the flesh and the Spirit. Victory comes as we reckon the old self to be dead and yield ourselves to Him, allowing His Spirit to rule. That is how a quick temper is softened and a restless heart is made calm.
Pray that your sister will come to know Jesus more deeply or to trust Him fully if she has not yet done so, for that is the source of peace. Pray that she will learn to keep her mind stayed on Him throughout the day, to bring every irritating moment to Him in prayer, and to choose the way of peace. Pray that the Lord will fill her heart with His Spirit so that instead of being easily provoked, she will show patience and gentleness, and that temptation will not overtake her but she will walk in self control.
May the Lord answer your prayer for her. May He grant her forgiveness and peace with Himself through Christ, and then that steady, perfect peace within that keeps her heart and mind. May He dispel fear and irritation and give her confidence that He is in control, so that she may be calm inside and out, and be a sower of peace in her home and in every argument she faces. In Jesus name, amen.