Unfaithful wife means faithless nation.

Hosea 2:1:15
Rebuke your mother, rebuke her, for she is not my wife,  and I am not her husband. Let her remove the adulterous look from her face and the unfaithfulness from between her breasts.
I will punish her for the days she burned incense to the Baals; she decked herself with rings and jewelry, and went after her lovers, but me she forgot,” declares the Lord.
Therefore I am now going to allure her;  I will lead her into the wilderness and speak tenderly to her.
There I will give her back her vineyards,  and will make the Valley of Achor a door of hope.
There she will respond as in the days of her youth, as in the day she came up out of Egypt.
Unfaithful wife - faithless nation.
Hosea's voice, pleading with his unfaithful wife, because one with the voice of God addressing Israel. The people are worshipping Baal, the Canaanite fertility god, thinking he is the one who gives good crops and plentiful harvests; when all the time it is God. They will be punished.
Why?
Israelite forgot that the Lord is the provider of their living. God had led them out from Egypt and entered the promised land. But now they turn away to Baal. it makes the Lord angry and let them go their way, let them be destroyed by their lover, foreign countries.
But God is full of mercy, when Israel is be rooted and moved to other places, God's mercy and grace will come over them again.
How?
God's love is everlasting love to those who love the Lord.