Is it permissible for the father to order the mother to cut off her relationship with her daughter because of the hijab, and is the mother entitled to sever ties of kinship with her daughter in this case, and is she sinful if she speaks to her without the father's knowledge?

The hijab is obligatory for a mature woman, and cutting off kinship ties is a grave sin. The father has no right to order the mother to cut off her relationship with her daughter, and it is not permissible for the mother to obey her husband in this act of disobedience. The daughter must continue to show piety towards her father and treat him kindly, as long as he does not command disobedience to Allah.