There is a lot packed in these 5 verses of chapter 3! The point of view changes in chapter 3: from a 3rd person narrative to a 1st person.
“The Lord said to me, ‘Go show love to your wife again,’” (v1) This is the Lord speaking directly to Hosea (“me”.) Hosea is called to go love his wife, Gomer, just as God has loved unfaithful Israel.
“although she is loved by another and is an adulteress. Love her as the Lord loved the Israelites, though they turn to other gods and love the sacred raisin cakes.” (v1) Just a note: Raisin cakes were used in the sacrificial feasts to the other gods.
In verse 2, it looks like Gomer had become a man’s slave: “So, I bought her back for fifteen shekels of silver and about a homer and lethek of barely.” A female was worth 30 shekels (“for a female, set her value at thirty shekels;” Leviticus 27:4) and Hosea paid for her with silver and barely. The fact that Hosea was able to pay for her with half silver and half produce means that she had become someone’s property and he used barely (not wheat) the coarsest kind of produce: shows how worthless Gomer was to her owner.
Even though it seems like he had every reason to leave and forget about her, Hosea chases after Gomer. Goes as far as to buy her back: pays a price to redeem her although she has been anything but faithful to him as a wife.
“Then I told her, ‘You are to live with me many days; you must not be a prostitute or be intimate with any man, and I will live with you.” (v3) Many days: this was not forever. This means that there is something after: a future.
“For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future” Jeremiah 29:11
He also says “live with you.” It sort of seems a little cold. Like they will be roommates but no loving intimate husband-wife relationship
“For the Israelites will live many days without king or prince, without sacred stones, without ephod or idol.” (v4) God is punishing the Israelites for their unfaithfulness to Him. Just as Hosea is just “living with” Gomer, God is doing the same to His people. It would be a long time before Israel would get a leader.
“Afterward the Israelites will return and seek the Lord their God and David their king. They will come trembling to the Lord and to his blessings in the last days.” (v5) The Israelites repentance is envisioned and the people come back to worship The Lord and the king from the dynasty of David. Remember that Jesus comes from the line of David!