Thank you for sharing your heart and your prayer so openly. Your desire for holiness in your home and neighborhood and your desire for God to bring protection and righteousness is understood, and God hears every prayer offered in Jesus name.
There is a real spiritual conflict in this world. Scripture teaches that we are born into a conflict between good and evil, and we feel it within ourselves and see its painful results around us in suffering and struggle that comes from rebellion against God. In that conflict it is right to turn to the Lord for help and protection, and to trust that He will accomplish His purposes. Even when people fail, God does not fail. Yet when we respond to conflict with hatred or bitterness, we are the ones who suffer loss.
That is why Scripture gives such a strong warning to watch over your own heart with diligence, lest any root of bitterness spring up to trouble you and defile many. Bitterness is not something that simply happens to you. It is an attitude you choose in response to difficult circumstances. Two people can go through the same hardship and one becomes better while the other becomes bitter. Bitterness only hurts you. It brings forth bitter fruit in your whole life and tightens and hardens you. The example of Esau is given for this reason. He did not repent at all, but became embittered and full of anger and hatred, and that root of bitterness continued through his descendants. Another example is the man who had followed and admired the work of God but was still found to be in the gall of bitterness and the bond of iniquity, bitter that he was no longer honored. He was told to pray that God would forgive him. God calls us to follow peace with all people and to guard our hearts from that kind of root.
Jesus taught that the first and greatest commandment is to love God with all your heart, soul, mind and strength, and the second is like it, to love your neighbor as yourself. Upon these two hang all the law and the prophets. Love does no harm to a neighbor, therefore love is the fulfilling of the law. You do not need to learn to love yourself more in order to love your neighbor. You already care for yourself, feeding yourself and clothing yourself and providing a roof over your head. You are called to love your neighbor in that same practical way, seeking his good and showing mercy when he is in need.
When a lawyer asked Jesus who is my neighbor, seeking to justify himself, Jesus answered with the story of the man who was robbed and wounded on the road from Jerusalem to Jericho. A priest and a Levite passed by, but a Samaritan showed mercy, bound his wounds and cared for him. Jesus then asked which of the three proved to be a neighbor, and the answer was the one who showed mercy. Go and do likewise, He said. Your neighbor is the person in need whom God has placed near you.
This helps to shape how to pray for the woman and children next door. God does not call you to use Scripture as a formula to root out or curse people you see as enemies, or to speak of children as weapons formed against you. He calls you to love your neighbor as yourself and to pray for their good. It is right to pray that any sexual sin outside of the lifelong covenant of one man and one woman in marriage would be brought into the light, that witchcraft and every work of the flesh which includes sexual immorality, impurity, idolatry, witchcraft, hatred, strife and envy would be dismantled, and that those trapped in such things would find true freedom in Christ. Jesus said if the Son sets you free you will be free indeed. That freedom is what she and her children need most, salvation through Jesus alone and a transformed life.
Resisting the devil, as James teaches, begins with submitting yourself to God. Binding and loosing, as Jesus taught in Matthew, is given in the context of the church seeking restoration and forgiveness, not as a way to place a curse on a neighbor or to transfer blame. Vengeance belongs to the Lord, as Romans teaches. Your part is to not return evil for evil, to keep your heart free from bitterness and slander, and to trust God to visit and to judge with perfect justice while you pursue peace.
It is also right to pray Psalm 91 for protection over your household and your neighborhood, and to ask God to guard your heart from any foothold of resentment. But the most powerful prayer you can pray for your neighbors is for their deliverance in the biblical sense, that God would draw the mother to repentance and faith in Jesus, that He would protect and provide for the children, and that He would make you an instrument of His mercy rather than of condemnation. Bad company does corrupt good character, so be wise and guard your home, yet do not dehumanize those next door. They are people made in God's image who need the same grace you need.
May the Lord keep your heart from bitterness, fill you with love for God and for your neighbor, and use your prayers and your kindness to bring His light into that home. Pray that God would save, cleanse and restore, that He would protect the innocent, and that He would give you wisdom to walk in love and holiness right where you live.