Let us stand in the gap for your brother and mother, seeking God's intervention and healing in their lives. We know that God is faithful and that His desire is for all to come to the knowledge of the truth and be saved.
Firstly, we must acknowledge that the only way we have access to God is by the name of Jesus. "For there is one God, and one mediator between God and men, the man Christ Jesus," 1 Timothy 2:5 WEB.
In regards to your estranged mother:
"Do not be deceived. 'Evil companionships corrupt good morals.' " 1 Corinthians 15:33 WEB. This applies not only to friends but to family as well. We must not support or enable sin, as difficult as it may be. Instead, we should encourage one another towards righteousness. "As iron sharpens iron, so a man sharpens the countenance of his friend." Proverbs 27:17 WEB.
We pray that your mother will seek God's will and find the strength to support your brother in a godly way, not by enabling his addiction but by encouraging him towards repentance and healing. Let us pray for her salvation and growth in the knowledge of Christ, that she may become a true disciple who worships God and ministers in prayer.
Regarding your brother:
"Put on therefore, as God's chosen ones, holy and beloved, a heart of compassion, kindness, lowliness, humility, and perseverance; bearing with one another, and forgiving each other, if any man has a complaint against any; even as Christ forgave you, so you also do. " Colossians 3:12-13 WEB.
We must remember that no one is beyond the reach of God's grace and mercy. Let us pray fervently for your brother's deliverance from drug addiction, that the Holy Spirit will convict him of his sin and lead him to repentance. We trust that you know the name of Jesus and that you can use it. If not, we will pray for your salvation as well.
"He who conceals his sins doesn't prosper, but whoever confesses and renounces them finds mercy. " Proverbs 28:13 WEB.
Heavenly Father, we come before You in the name of Jesus, lifting up this brother who is bound by drug addiction. We pray for his deliverance and healing, that the chains of addiction will be broken in his life. We rebuke the spirit of addiction and command it to leave in the name of Jesus. We also pray for his mother, that she will seek Your will and find the strength to support her son in a godly way. We ask that You will bring healing and restoration to their relationship, and that both of them will come to a saving knowledge of Jesus Christ. We ask this all in accordance with Your will, in Jesus' name, we pray. Amen God.