Is it the husband's right, Islamically, to know everything that is discussed between his wife and her mother in his home, or even over the phone, claiming he is the master of the house?

It is not the husband's right that his wife inform him of every single matter concerning her. Thus, there is no blame upon her if she speaks with her mother or another person privately, and the husband has no right to prevent her from doing so, nor is she obliged to tell him what they discussed. Nevertheless, it is advised to avoid anything that leads to discord between the spouses.