The OP is correct, but a few clarifications are needed:
God divorced the House of Israel (10 tribes).God scattered them amongst the nations, God had no mercy on them, and God told them they were not a people.
In Hosea, it was said that one day God would return to them, and tell them that they were a people.
That promise happened when the New Covenant was made with the shed blood of Christ Jesus on the cross. Peter confirms the Hosea promise (1 Peter 2:10).
Because the Israelites were scattered amongst the Gentiles for over 700 years, they became like Gentiles, and by the time the first century came, most of the Israelites from the 10 tribes could not be distinguished from a pagan Gentile.
The gospel went to the Jew first, then the Gentile. That is how all of Israel was saved, and that is how the promise of a New Covenant to both houses was fulfilled.
All who have faith in Christ Jesus are the sons of Abraham, the Israel of God.