What should I do about my sin with a married woman, and should I apologize to her husband despite my fear of destroying their home?

The temptation of women is great, and the Prophet, peace and blessings be upon him, warned against it. Satan strives to mislead people. So, praise your Lord and hasten to sincere repentance for what you have done. You have wronged the husband of this woman by betraying him in his honor. The original principle is that you should seek his forgiveness, but some scholars have permitted suffices with repentance in matters of intangible rights if there is fear that informing the right-holder would lead to greater harm. So, repent between yourself and your Lord, and pray for good for this man and his wife, and increase in righteous deeds, and avoid temptation and its causes.