Hosea started his ministry when Jeroboam II was king of Israel/Samaria and Uzziah was king of Judah. He continued for about 50 years, until the time of Hezekiah. It’s been suggested that Hosea fled to Judah during or shortly after Jeroboam’s reign, and so he acknowledged only the Judean kings.
The focus of Hosea’s ministry was almost entirely on Israel:
Hosea 1:2 When the Lord first began speaking to Israel through Hosea, he said to him, ‘Go and marry a prostitute, so that some of her children will be conceived in prostitution. This will illustrate how Israel has acted like a prostitute by turning against the Lord and worshiping other gods.’
What faith Hosea must have had to be able to follow such a command.
How deeply God must have felt about His chosen people turning away from Him as they did.
Even so, God holds out a promise of redemption:
Hosea 3:1-5 Then the Lord said to me, ‘Go and love your wife again, even though she commits adultery with another lover. This will illustrate that the Lord still loves Israel, even though the people have turned to other gods and love to worship them.’ So I bought her back … This shows that … the people will return and devote themselves to the Lord their God and to David’s descendant, their king. In the last days, they will tremble in awe of the Lord and of his goodness.
That Bible blog 