What is the ruling of the Sharia regarding boycotting one's parents – while maintaining daily phone contact with them – due to their expulsion of their two daughters from the home and their insistence that they apologize to the oppressive, tyrannical daughter-in-law?

If the situation is as described, regarding the sister-in-law's injustice and your parents expelling you because you demanded an apology from her, then the parents' action is incorrect and oppressive. However, if there is no harm to you in seeking forgiveness, then you must obey your parents. Forgiving an aggressor increases one's honor and dignity, and it is a path to attaining Allah's pardon and forgiveness.