In the book of Hosea, distinctions are made. The major distinction is between The House of Judah and the The House of Ephraim/The Northern Kingdom. Judah is mentioned as retaining her position before God. It is The House of Ephraim, which signifies The Northern Kingdom that this book is about, not Judah.
It is The House of Ephraim which is lost into the gentile world, no longer subject to God's mercy, no longer His people, utterly scattered, lost and forgotten. It is at the end of time that the people descendant from the children of The House of Ephraim are once again identified, brought into Israel, and take again their rightful identities as true Israelites.
This book is primarily about The Northern Kingdom, not Judah. Judah has a totally different destiny, taken to Babylon, with a remnant brought back to rebuild The Temple and Jerusalem. Their descendants became the Judites of Jesus time and His parents. The Jews/Judites never lost their identity as the children of Israel. The people of God of The Northern Kingdom did.
The people of The Northern Kingdom and their descendants have been siphoned into the Church, and also will be found at the end of the age and brought back to Israel as true Israelites. They are those who were not My people, who shall be called the people of God again.
We are to rightly divide The Word of God. One extremely important division is between The Southern Kingdom and The Northern Kingdom. Much of The Bible, to be rightly understood, is about these two Kingdoms finally and once again becoming one.
you are right, although I believe that the destruction of the Temple and the scattering and re-birth of the nation of Israel from 70 ad -1948 are also anticipated in Hosea three.