We understand your concerns about your neighbors, and we empathize with the difficulties you're facing. Let's bring your situation before the Lord in prayer and seek His will according to His word.
Firstly, we commend you for acknowledging Jesus Christ as the only one with the power to intervene. It is only by the name of Jesus that we can approach God.
Remember what the WEB says in Romans 13:1-2, Let every soul be in subjection to the higher authorities, for there is no authority except from God, and those who exist are ordained by God. Therefore he who resists the authority, withstands the ordinance of God; and they who withstand will receive to themselves judgment.
And God tells us how to live with unbelievers in 1 Peter 2:11-17, Beloved, I beg you as foreigners and pilgrims to abstain from fleshly lusts, which war against the soul; having your behavior honest among the Gentiles, that when they speak against you as evil-doers, they may see your good works and glorify God in the day of visitation. Therefore subject yourselves to every ordinance of man for the Lord's sake: whether to the king, as supreme; or to governors, as sent by him for vengeance on evildoers and for praise to those who do well. For this is the will of God, that by well-doing you should put to silence the ignorance of foolish men: as free, and not using your liberty for a cloak of wickedness, but as bondservants of God. Honor all men. Love the brotherhood. Fear God. Honor the king.
We also need to remember God's command to love, forgive and pray for those who wrong us.
Matthew 5:43-45, You have heard that it was said, "You shall love your neighbor, and hate your enemy." But I tell you, love your enemies, bless those who curse you, do good to those who hate you, and pray for those who mistreat you and persecute you, that you may be children of your Father who is in heaven. For he makes his sun to rise on the evil and the good, and sends rain on the just and the unjust.
Now, let us pray together:
Dear Heavenly Father, we come before You in the name of Jesus Christ, lifting up our fellow believer who is facing distress due to ungodly neighbors. Lord, You know the challenges they are facing, the fear, and the unhappiness that has been brought to their home. We pray for Your intervention, that You would bring peace and safety to their home. We ask that You would change the hearts of these neighbors, that they may know Your saving grace. Convict them of their sinful behavior, and draw them to repentance. If it is Your will, Lord, remove them from the vicinity, but we also pray that You would be merciful to them, not blotting out their sins, but turning them from their wicked ways. We ask for justice, but also for mercy. We call on you to protect this family, physically, emotionally, and spiritually.
Now Lord let us be sure that we are in right standing with you too. In Jesus' name, we pray and rebuke any evil spirits in the neighbor's lives causing this turmoil. Lord, help us to be forgiving and loving, even when it's difficult. Thank you Jesus for hearing and answering our prayers and thank you for the power of the Holy Spirit working in us. Amen.
We encourage you using Psalm 34:12-14, What man is there who desires life, and loves many days, that he may see good? Keep your tongue from evil, and your lips from speaking deceit. Depart from evil, and do good. Seek peace, and pursue it.
Let us also remember that God is our refuge and strength, a very present help in trouble and not to fear even if the world is changing. God is in control over all things including governments, authorities, and neighbors.
Continue to seek God's will in this situation, trusting that He will bring about what is best for you and your family.
Prayer Focus: God, Thank You for loving me. God, I ask You in Jesus’ name please bless me with everything that I stand in need of and everything You want me to have. 
