Paul contrasts two covenants--that from Sinai, and the new covenant (implied) that is connected with the heavenly Jerusalem, and Sarah the wife of Abraham
Yes, but before the covenant from Sinai, where the people said, give us the law and we will follow it [they didn't], we have the everlasting covenant with Abraham, where God made the covenant between himself and himself [Abraham's seed], the covenant of the promise. That covenant comes down through Abraham, Isaac, Jacob, and Ephraim. Ephraim, the house of Israel, are the children of the promise [they will be called sons of the living God].
The story of the prodigal son could be applied to house of Judah and house of Israel. Any reason why not?
11And he said, A certain man had two sons: two sons: house of Judah, house of Israel
13And not many days after the younger son gathered all together, and took his journey into a far country, and there wasted his substance with riotous living. house of Israel disappears into the gentile countries and lives like a gentile [squanders his wealth as a son]
15And he went and joined himself to a citizen of that country; and he sent him into his fields to feed swine.house of Israel loses its identity. Joins the gentiles. Sloping the pigs in a gentile country.
18I will arise and go to my father, and will say unto him, Father, I have sinned against heaven, and before thee,
19And am no more worthy to be called thy son: make me as one of thy hired servants. House of Israel decides to repent and return to Father as a servant
22But the father said to his servants, Bring forth the best robe, and put it on him; and put a ring on his hand, and shoes on his feet:
23And bring hither the fatted calf, and kill it; and let us eat, and be merry: Father dresses the house of Israel in the robe and signet ring of a king and orders a huge party to celebrate his return. The mystery is revealed to him [the Gentiles.]
24For this my son was dead, and is alive again; he was lost, and is found. And they began to be merryhouse of Israel was lost [into a gentile identity] and is now found. House of Israel told he is a son.
29And he answering said to his father, Lo, these many years do I serve thee, neither transgressed I at any time thy commandment: and yet thou never gavest me a kid, that I might make merry with my friends:
30But as soon as this thy son was come, which hath devoured thy living with harlots, thou hast killed for him the fatted calf. house of Judah [older faithful brother] is angry because he has done all the right things and stayed with his Father and kept the law and the Temple while the younger son was out playing and slopping the pigs and acting like a gentile.
31And he said unto him, Son, thou art ever with me, and all that I have is thine.The Father assures the house of Judah that he is still a close son and an inheritor but says of his younger son:
32...: for this thy brother was was dead, and is alive again; and was lost, and is found.house of Israel, the younger son has returned to the family and thus is now alive.