What is the correct Islamic action that the sister should take in this situation, knowing that she honors her parents and sisters and works for their sake, but her sisters hate her and expel her from the house?

The questioner's care for her mother and sisters falls under the reward for caring for a widow and sponsoring an orphan. This is considered an act of filial piety towards her father after his death. Her reward will be multiplied by seeking recompense from Allah and by her patience with the ingratitude of her sisters, and by not reciprocating their behavior. The sister was urged to find out the reason for their animosity and to confront them about it. It was also suggested that she seek help from her mother or a relative to resolve the dispute. She was also called upon to help her husband build a private residence for themselves.