We are truly saddened to hear about the situation your daughter is in, and we are here to pray and provide biblical guidance with you. Firstly, we thank you for submitting your request in Jesus' name, as it is only through His name that we have access to the Father (John 14:6).
We strongly urge you to take comfort in the promises of God. There are multiple issues we need to pray about. One is the belief of the guy and the other is about the future of your daughter and the decisions she makes in this relationship.
It is important that we understand that God does not approve of relationships that are not equally yoked. In 2 Corinthians 6:14 WEB it says, Do not be unequally yoked with unbelievers, for what fellowship have righteousness and iniquity? Or what fellowship has light with darkness? We see that God's word clearly warns us against being in close relationships with unbelievers, especially when it comes to romantic relationships. We also need to pray for your daughter as she needs to consider the reasons she has chosen someone who does not have her best interests in mind. We need to pray for her faith and that she chooses to seek God's will. We need to pray for the guy as well in his spiritual condition and that God would intervene in his life so that he may become a believer. This should be our main concern as we pray in this situation.
Regardless of the details, the fact that this man is manipulative, paranoid, and controlling is a clear indication that this relationship is not healthy or godly. In Ephesians 5:25-29 WEB, we see the instructions for husbands to love their wives as Christ loved the church, and for men to nourish and cherish their wives. This is not the picture you have painted of this man.
Let us pray together:
Heavenly Father,
We come before You in the mighty name of Jesus, pleading for Your intervention in the life of our dear sister and her daughter. Lord, You know the situation better than anyone, and You alone have the power to change hearts and turn this situation around.
First, Lord, we pray for the salvation of this man. We pray that You would reveal Yourself to him in a powerful way, that he would come to know You as his Lord and Savior. We pray that You would convict him of his sins and turn him away from his manipulative and controlling behavior.
Second, Lord, we pray for our sister's daughter. We ask that You would strengthen her faith and give her the courage to stand up for what is right. We pray that You would open her eyes to see the truth about this relationship and that You would give her wisdom in how to proceed.
We rebuke the enemy's attempts to destroy her life and separate her from You and Your church. We ask You, Lord, to surround her with godly counsel and support, and to guide her steps according to Your will.
Lastly, Lord, we pray for our sister. We ask that You would comfort her and give her peace in this difficult time. We pray that You would guide her as she supports her daughter, and that You would use this situation to bring their family closer to You.
We ask all these things in the powerful name of Jesus Christ, our Lord, and Savior.
Amen.
Lastly, we encourage you to stand firm in your faith and to continue to pray fervently for your daughter and this situation. Remember the promise in James 5:16 WEB, that The effective, earnest prayer of a righteous man accomplishs much. Trust that God is at work, even in the midst of this trial. Do not be afraid to make the situation clear to your daughter. Also, consider seeking wise counsel from your church leaders or other mature believers in your life.
Remember we are here to support you.
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. 
