What should I do about a person who tests me in my work, my home, and my children, knowing that I fear sin and the torment of hellfire if I were to kill him, so what is the way out if he persists in his actions?

It is not permissible to commit suicide, which is the taking of a life that Allah has forbidden, due to harm. The punishment for intentionally killing a believer is Hell, wherein one will abide eternally, along with Allah's wrath and curse upon him. This is far greater than any current hardship. The Sharia (definition) permits the wronged person to retaliate with the equivalent of the aggression inflicted upon them, as Allah Almighty says: "So whoever commits aggression against you, then aggress against him in like manner as he aggressed against you," and "The recompense of an evil deed is an evil deed like it." The questioner should seek assistance from state authorities to avert the harm. If unable to do so, then patience is required, for its outcome is praiseworthy, and Allah is with the patient.