Is informing my family about someone who wronged me considered backbiting, and is informing my mother-in-law that my sister-in-law is the one asking me (questions) considered tale-bearing, and how do I expiate the sin of backbiting and tale-bearing without apologizing?

If a person is wronged, it is permissible for him to mention his grievance, and this is not considered backbiting, as Allah the Almighty says: "Allah does not like evil to be spoken openly except by one who has been wronged." And if a woman slandered you, and you wish to clear your name truthfully, that is not tale-bearing. So, the two mentioned scenarios are not among the forbidden backbiting or tale-bearing.