We are truly saddened to hear about the struggles your family is facing, but we are grateful that you have reached out for prayer and support.
We are going to claim the Lord Jesus and His absolute power over the situation with your brother, his mental illness, and the challenges your family is facing. Let us remember that our battle is not against flesh and blood, but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms. Ephesians 6:12 WEB.
First, we acknowledge that God is the ultimate healer. Psalm 147:3 WEB tells us that "He heals the broken in heart, and binds up their wounds." We pray for your brother's mental healing, that God would touch his mind and heart, and bring peace and stability to his life.
We must also recall I John 1:9 WEB If we confess our sins, he is faithful and righteous to forgive us the sins, and to cleanse us from all unrighteousness. This passage is often used to encourage us to confess sin. However, the passage is better understood if we realize that the Greek word used here for confess literally means to agree with God. This passage could be translated "If we agree with God concerning our sins" Furthermore, it is not talking about individual sins, but agreeing with God about the fact that we are sinners with a sin nature. This is the opposite of denying that we are sinners or have a sin nature.
We pray that your brother and mother and all of your family agree with God about this and believe the gospel message of Jesus Christ. We pray for your brother's salvation, that he would come to know Jesus Christ as his personal Lord and Savior.
Next, we address the outbursts and irrational behavior. Galatians 5:22-23 WEB tells us that the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faith, gentleness, and self-control. We pray that your brother would be filled with the Holy Spirit and exhibit these fruits, especially peace, patience, and self-control.
We rebuke the spirit of irrationality and emotional instability that has taken hold of your brother. We command it to leave in the name of Jesus Christ and we claim that your brother will have a calm mind and self-control in his actions.
We also pray for your mother's protection, strength, and peace. Psalm 91:1-2 WEB says, "He who dwells in the secret place of the Most High will rest in the shadow of the Almighty. I will say of Yahweh, 'He is my refuge and my fortress; my God, in whom I trust.'" We pray that your mother would find refuge, strength, and peace in God, and that He would surround her with His divine love and protection especially when dealing with your brother.
Lastly, we pray for unity and healing in your family. Colossians 3:14 WEB tells us, "Above all, put on love, which is the bond of perfection." We pray that love would bind your family together and that God's healing power and divine love would surround and fill your family.
We agree with you and claim all of these things in the name of Jesus Christ.
We would also like to encourage you to seek professional help for your brother, as mental illness often requires medical intervention alongside spiritual support. The scriptures tell us that we should not neglect modern medicine. When the apostle Paul instructed Timothy to drink a little wine to help with his stomach malady, Paul was acknowledging the value of medicine. We pray for God's wisdom and guidance as you navigate this situation.
Lastly, we want to remind you that God is faithful, and He cares for you and your family. Cast all your anxieties on him, because he cares for you. I Peter 5:7 WEB. Keep holding on to faith, hope, and love.
Prayer Focus: God, Thank You for loving me. God, I ask You in Jesus’ name please bless me with everything that I stand in need of and everything You want me to have. 
