God used the names of Hosea's three children as object lessons for the nations of Israel and Judah. He also used Hosea's marriage to Gomer as an object lesson. God had a bigger purpose in mind. Hosea willingly obeyed the Lord, and the prophetic message went to the Hebrews and endures forever in scripture.
But I feel compassion toward this little girl born around 750 B.C. I want to imagine that Hosea loved his (only?) daughter with great tenderness and strength. Surely she needed the warm, loving embrace of her father, and surely Hosea found the time and heart to show her God's love. Apparently she would never find that attention from her mother.
My point is that we don't always understand what God is up to. When he leads us into dark places and situations we want to avoid, we need to shine his light even brighter.