Can my wife return to me after I divorced her three times, do I bear sin for divorcing her, and how can I atone for my sin?

A wife's request for divorce without cause is forbidden by Islamic law, as is the involvement of her guardians in such a request. As for the divorce pronouncement: "You are divorced, divorced, divorced," if you intended it as an emphasis, then it is considered a single divorce, and you may take back your wife as long as she is within her waiting period (iddah (definition)), provided this was the first or second divorce. However, if you intended to initiate a divorce with each utterance, then your wife has become irrevocably divorced from you with a major separation (baynunah kubra), and she is not lawful for you until she marries another husband, as Allah the Almighty says: "And if he has divorced her [for the third time], then she is not lawful to him afterward until she marries another husband."