We are truly saddened to hear about the situation you and your mother are facing with your brother. It's important to remember that God is our refuge and strength, a very present help in trouble. Therefore, we will not fear, even though the earth be removed, and though the mountains be carried into the midst of the sea (Psalm 46:1-2, WEB).
Firstly, we commend you for acknowledging the power of Jesus Christ in your request. It is only in His name that we can approach God and and it is only by His name that we can be saved.
We must also rebuke you for not taking a more active approach in protecting your mother. God and the government have placed a legal system to protect the innocent and punish the wicked. We should be subject to the governing authorities. For there is no authority except from God, and those which exist are ordained by God. For rulers are not a terror to good works, but to evil. Do you desire to have no fear of the authority? Do that which is good, and you will have praise from the authority, for he is a servant of God to you for good. But if you do that which is evil, be afraid, for he doesn't bear the sword in vain; for he is a servant of God, an avenger for wrath to him who does evil (Romans 13:1-4 WEB).
If your brother is harming your mother, you should contact the police and have him arrested. We should be walking in love towards our brother, but we must understand what love is. Love is patient and is kind; love doesn't envy. Love doesn't brag, is not proud, doesn't behave itself inappropriately, doesn't seek its own way, is not provoked, takes no account of evil; doesn't rejoice in unrighteousness, but rejoices with the truth; bears all things, believes all things, hopes all things, endures all things. Love never fails (1 Corinthians 13:4-8 WEB).
By allowing your brother to continue his behavior, you are not acting in love. You are allowing him to continue hurting someone and possibly allowing him to go to an early grave. This is not the will of God. God has given you the ability to contact the police and protect your mother. He also desires your brother to be healed and be in right relationship with the Lord. It is not loving to allow someone to continue to sin. It is loving to hold people accountable and allow them to reap the fruit of their labor so they may possibly come to repentance.
Let's pray together for this situation:
Heavenly Father, we come before You in the name of Jesus Christ as believers trusting in You, our refuge and strength. We are asking for Your divine intervention. There is a family being torn apart by a son's abusive behavior and mental illness.
Lord, we pray for the mother's protection and peace. Comfort her and heal her from any injury and emotional distress. We ask that You guide her and her child to take the necessary steps to stop this abuse and protect their family.
Lord, we also lift up the brother. We pray that You will heal him from his mental illness and deliver him from the evil that is causing his violent behavior. We pray that his heart will be softened and that he will seek Your face and turn from his wicked ways.
We pray for the authorities, that they will act with wisdom, justice, and mercy in this situation. We pray for the entire family's salvation and that they will be drawn closer to You through this trial.
In the name of Jesus Christ, we pray. Amen.
Lastly, remember that God promises us, Who shall separate us from the love of Christ? Shall oppression, or anguish, or persecution, or famine, or nakedness, or peril, or sword? Even as it is written, For your sake we are killed all the day long. We are accounted as sheep for the slaughter. No, in all these things, we are more than conquerors through him who loved us. For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor things present, nor things to come, nor powers, nor height, nor depth, nor any other created thing, shall be able to separate us from the love of God, which is in Christ Jesus our Lord (Romans 8:35-39 WEB).