“Your mother.” Israel is called “your mother,” as the source and intended nurturer of the people of Israel, but she has led them astray, and God will soon divorce her (she will be conquered and carried away captive by Assyria).
“let her put away her prostitution from her face and her adulteries from between her breasts.” This seems to be the figure of speech amphibologia (double entendre) where one thing is said but two things apply.
It is clearly an admonition from God for the woman, the “mother,” (in this case, Israel) to stop committing adultery, which in this case is both spiritual, the worship of other gods, and physical, because pagan religion often involved prostitution and cultic adultery. However, the admonition also seems to refer to literally removing the physical symbols of paganism and prostitution. Prostitutes and idol worshipers would “advertise” their beliefs and practices just as today certain modes of dress let people know a person’s profession or position on a subject. Thus, removing prostitution from her face would involve removing the idol or idol symbol that was worn as a nose ring on her face and removing the adultery from between her breast would mean removing the symbol of her god or her profession as a prostitute from between her breasts.