We are truly saddened to hear about the challenges your family is facing, and we are here to intercede for you and to provide biblical guidance.
Firstly, we commend you for acknowledging the power of Jesus Christ in your request. The Bible tells us we have access to God in prayer because of the sacrifice of Jesus Christ. In John 14:13-14 Jesus promises, "Whatever you will ask in my name, that will I do, that the Father may be glorified in the Son. If you will ask anything in my name, I will do it." It is only by the name of Jesus that we have access to God.
Let's address the specific issues you mentioned. It's important to understand that God desires that everyone be saved and come to the knowledge of the truth (1 Timothy 2:3-4). Salvation is a deeply personal choice, and while we can pray for your family, each individual must make their own decision to follow Jesus. We pray that the Holy Spirit will convict their hearts and draw them to Christ.
Regarding your mother's health and behavior, it's crucial to remember the biblical commandment to honor our parents (Exodus 20:12). This can be challenging, especially when they are being disobedient and ungrateful. However, we are called to respond with love and patience, even in difficult situations. In Ephesians 4:31-32, the Apostle Paul writes, "Let all bitterness, wrath, anger, outcry, and slander, be put away from you, with all malice. And be kind to one another, tenderhearted, forgiving each other, just as God also in Christ forgave you."
The issues of division, discord, and what you described as an "extermination spirit" in your family need to be addressed spiritually. These are signs of spiritual warfare, and we must pray fervently against these forces. In Ephesians 6:12, Paul reminds us, "For our wrestling is not against flesh and blood, but against the principalities, against the powers, against the world's rulers of the darkness of this age, and against the spiritual forces of wickedness in the heavenly places."
Let us pray together:
"Father in heaven, we come before You in the name of Jesus Christ, lifting up this family to You. We pray for their salvation, that each member would come to a saving knowledge of Jesus Christ. We pray for healing, both physical and spiritual, especially for the mother who is ill and struggling. Lord, soften her heart and help her to be obedient and grateful.
We rebuke the spirits of division, discord, and extermination that are affecting this family. In the name of Jesus, we command these spirits to leave and we claim unity, peace, and love in their place. Father, provide for their needs according to Your riches in glory. Help them to be a light in this world, a family that honors You in all they do.
In Jesus' name, we pray. Amen."
Continue to stand firm in your faith and trust that God is working in your family's life. Be a beacon of light and love, and remember that with God, all things are possible (Matthew 19:26).
Prayer Focus: God, Thank You. Thank You for loving me. God, I ask You in Jesus’ name bless me with everything that I stand in need of and everything You want me to have. Bless me to know You in truth, fall in love with You with all my heart, mind, soul, body, and strength and never fall out of love with You. Bless me to have an ever growing closer stronger, more intimate relationship with You. Bless me with the love, desire, strength, and the spirit of obedience to always delight myself in You, seek first Your kingdom, and Your righteousness. Help and strengthen me God to always respect and obey You. Bless me to trust You with all my heart, acknowledge You in all my ways, and lean not to my own understanding. 
