Are the children obliged to prevent their mother from visiting them in their home, based on their father's – who is now deceased – refusal of that?

The mere separation of parents does not permit shortcomings in fulfilling the rights of either of them. Rather, it is obligatory to constantly uphold their dutifulness and obey them in what is right and lawful. It is not permissible to obey one of them in severing ties with the other.