Is the woman who was expelled from her home and verbally abused by her mother-in-law considered sinful for severing ties with her, given that the mother-in-law initiated the estrangement, and will the woman's good deeds be accepted despite this severed tie?

Your mother-in-law does not have the right to expel you from her house, and your husband must prevent her from doing so. It is better for you to forgive her and overlook her mistakes, and to treat her kindly, for Allah Almighty says: "Repel evil with that which is best, and lo, he between whom and you was enmity will become as though he were a devoted friend." You should also apologize to her and resolve the disagreement between you. By doing so, you will please your husband and help him honor his parents. If you fulfill your duty by visiting her and greeting her, you will have cleared yourself of any blame.