With whom should they quarrel?
Rashi: With your current Kenesiyah (assembly), which is the mother of coming generations.
Radak: Keneses Yisrael was compared to a Zonah, and those born in every generation to Yaldei Zenunim. He tells the children to quarrel with their mother. The Kenesiyah is compared to a mother, like the Klal, and the individuals to children. The idea is, man will quarrel with his colleague to return him to the good path.
Malbim: You children should rebuke your mother for her Zenus; she should improve her ways. As long as she is not My wife, and she is Mezanah in back of Me, I am not her husband, and the children are not mine. This was Hashem's answer to Hoshe'a ? it is incumbent on the Nevi'im, including Hoshe'a, to quarrel with the mother (Kenesiyah) and rebuke her to improve her ways.
Why does it say "Ki Hi Lo Ishti"?
Radak: She was Mezanah under Me.
How will she remove her Zenus from her face?
Radak: Since Keneses Yisrael is compared to a Zonah, it mentions ways of Zonos ? they adorn their faces with colors, to appear beautiful in the eyes of men who are Mezaneh.
Radak (according to the Nimshal): The face is a Mashal for Nevi'im. The nation switched Nevi'ei Hashem (instead of heeding them, they go) for Nevi'ei Sheker.
Malbim: This is idolatry that she serves openly, to the point that matters of Zenus are seen on her face.
Why does it say "Na'afufeha mi'Bein Shadeha"?
Rashi: Female adulterers, [men] press between their breasts. Radak ? also Yechezkel said "Shamah Mo'achu Shedeihen" (23:3). Also this is the way of Zonos.
Rashi citing Targum Yonasan: Service of idolatry is between her walls.
Radak (according to the Nimshal): Shadayim are a Mashal for written and oral Torah, like I explained in Yechezkel. They switched them for idolatrous rites ? these are Na'afufim.
Malbim: This is lust for adultery hidden between her breasts ? the Yetzer ha'Ra for idolatry and Arayos.