What is the Sharia ruling regarding a wife who refuses to live with her husband and his children from his deceased wife in the same house, and wants complete separation from them, even in eating and drinking, while the children wish to live with their father and his wife in the same house, with separation only in sleeping quarters?

The stepmother does not have the right to prevent the children from visiting their father or socializing with him. However, it is her right that her husband provide her with an independent dwelling where she will not be subjected to harm or embarrassment. She has the right to refuse your living with her in your father's house and to have you separate at bedtime only. You can limit your time sitting with your father to what does not harm the wife, and through which your father's companionship is achieved.