How can one atone for a sin and find peace of conscience, and is there a sin of accidental killing of the wife, after she prayed for her husband's death, so he prayed for his own death, and she fears that God will answer his prayer?

It is not permissible for a woman to say words to her husband that vex him, nor is it permissible for the husband to supplicate against himself, as the Prophet, peace and blessings be upon him, forbade that. The wife's words are not considered a cause of murder, and there is no sin upon her unless she intends harm. Both spouses are advised to remember Allah and seek His forgiveness.