I'm seeing Hosea 1:11 as the two separate Houses, House of Judah and House of Israel. Jesus is that one head who will bring the two houses back together again. This is how I am understanding a multitude of verses that put the story together.
Hos 1:11 Then shall the children of Judah and the children of Israel be gathered together, and appoint themselves one head, and they shall come up out of the land: for great shall be the day of Jezreel. (Jezreel is a play on Israel and yes wont that be a glorious day when Jesus is King over all the world, House of Judah and House of Israel once again reunited as they were during King David and King Solomon?
Rom 9:25 As he saith also in Osee, I will call them my people, which were not my people; and her beloved, which was not beloved.
God said He divorced the House of Israel. Thus, in Hosea they are no longer called "My People".
Jer_3:8 And I saw, when for all the causes whereby backsliding Israel committed adultery I had put her away, and given her a bill of divorce; yet her treacherous sister Judah feared not, but went and played the harlot also.
Can you see the mention of the two Houses here in this Jeremiah verse above?
Jeremiah seems to be puzzled how the LORD can have His divorced wife back again when it goes against the LORD's own Law.
Jer 3:1 They say, If a man put away his wife, and she go from him, and become another man's, shall he return unto her again? shall not that land be greatly polluted? but thou hast played the harlot with many lovers; yet return again to me, saith the LORD.
That Law is Deuteronomy 24:1-4. And I believe Paul was given understanding of this mystery and why Jesus said "
Mat_10:6 But go rather to the lost sheep of the house of Israel.
Mat_15:24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
And later Jesus gave the Caanite woman permission to eat bread crumbs from the master's table.
Mat_15:27 And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters' table.
Mar_7:28 And she answered and said unto him, Yes, Lord: yet the dogs under the table eat of the children's crumbs.
But here is Paul quoting the Deuteronomy 24:1-4 scripture.
Rom 7:1 Know ye not, brethren, (for I speak to them that know the law,) how that the law hath dominion over a man as long as he liveth?
Rom 7:2 For the woman which hath an husband is bound by the law to her husband so long as he liveth; but if the husband be dead, she is loosed from the law of her husband.
Rom 7:3 So then if, while her husband liveth, she be married to another man, she shall be called an adulteress: but if her husband be dead, she is free from that law; so that she is no adulteress, though she be married to another man.
Rom 7:4 Wherefore, my brethren, ye also are become dead to the law by the body of Christ; that ye should be married to another, even to him who is raised from the dead, that we should bring forth fruit unto God.
Deu 24:1 When a man hath taken a wife, and married her, and it come to pass that she find no favour in his eyes, because he hath found some uncleanness in her: then let him write her a bill of divorcement, and give it in her hand, and send her out of his house.
Deu 24:2 And when she is departed out of his house, she may go and be another man's wife.
Deu 24:3 And if the latter husband hate her, and write her a bill of divorcement, and giveth it in her hand, and sendeth her out of his house; or if the latter husband die, which took her to be his wife;
Deu 24:4 Her former husband, which sent her away, may not take her again to be his wife, after that she is defiled; for that is abomination before the LORD: and thou shalt not cause the land to sin, which the LORD thy God giveth thee for an inheritance.
Jesus is "God with us". Jesus is the Word and the Word became flesh. God could not break His own law, so He had to die and resurrect in order to bring back "the house of Israel" whom He divorced and promised in many of the scriptures that He would take her back again. Thus a New Covenant had to be made because God found fault with the people after they said the marriage vows (First Covenant) at Mount Sinai and then finally gave them up for a time. House of Israel was taken into captivity in 721/722 BC and unlike the House of Judah who was taken into captivity for 70 years by the Babylonians, and then returned to the land, but the House of Israel never came home, instead they are scattered to the four corners of the earth.
Ex.19:1-4
Exo 19:5 Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine:
Exo 19:6 And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel. (all 12 tribes).
Exo 19:7 And Moses came and called for the elders of the people, and laid before their faces all these words which the LORD commanded him.
Exo 19:8 And all the people answered together, and said, All that the LORD hath spoken we will do. And Moses returned the words of the people unto the LORD.
Jeremia 31:31-33 and Hebrews 8:8-11
Heb 8:8 For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
So where do the non-house of Israel and non-house of Judah people come into the kingdom? I'll save that one for later.