Have I committed a sin by relaying my brother’s wife’s offensive words to my mother, and will my repentance be accepted?

What the questioner did is forbidden backbiting (namimah), and she must seek Allah’s forgiveness and repent to Him, the Almighty, for His saying: "And whoever does evil or wrongs himself then seeks Allah’s forgiveness, he will find Allah Forgiving and Merciful," and for His saying: "Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.'" Part of the required rectification is for her to strive to mend the rift between her mother and her brother and his wife, and to endeavor to appease her mother towards them and elicit prayers from her for their guidance and betterment.