I can understand your struggle, and appreciate your attempt to follow the flow of Paul’s argument here.
To begin with, chapters 9-11 deal with the very important matter of the relationship of Jews and Gentiles in the church (in the New Testament age). The Jews tended to assume that they were “elect” as a nation simply because they were Jews, or, as they put it, because they were the children of Abraham (see Luke 3:7-9; also John 8:33ff.). In Romans 9:1-5 Paul begins by affirming his great love for his fellow-Jews. In verses 4-5 he enumerates some of the privileges of the Jews. In verses 6-13 Paul seeks to prove his point that not all Jews are “true Jews”; that is, not all Jews are believers. The Jews seemed to believe in corporate election, rather than individual election. Their view of election seems to be that God chose to save all Jews, but only a few Gentiles (and those Gentiles who were saved came into salvation by becoming Jewish proselytes). Paul shows that God did elect, but individually, as opposed to corporately. Thus, God chose Isaac, but not Ishmael, even though both were the sons of Abraham. Then, God chose Isaac’s son Jacob, but rejected Esau. This choice was made before the birth of the two boys. The choice was made independently of what either child would do, and thus their election wasn’t earned or merited in any way. In this sovereign choice, God even set aside the normal custom of making the oldest son the primary heir. (The older child ended up serving the younger.)
Before one can understand verses 14-26, he must understand that Paul taught God chooses some (Jews) but rejects others. God elects some, and not others.
In verse 14 an objection is raised, based upon Paul’s teaching of election in the previous verses. The assumption is that God must be unjust to elect some, but not others. “God is not unjust! How could He elect as you have said, Paul?” Paul responds, “May it never be that God is unjust, and He certainly is not!” God is Sovereign, and He can do as He chooses (compare Daniel 4:32, 34-35). God chose Moses for salvation, and to be the leader of the nation Israel. God chose Pharaoh to be an instrument to glorify Himself by his rebellion. (Pharaoh said, “Who is the God of Israel that I should obey Him?” — Exodus 5:2. God answered that question with the plagues and the exodus.) By his unbelief and rebellion, Pharaoh glorified God. God chose Moses for salvation, and Pharaoh for destruction. God is free to show mercy to whom He will, and to also is free not to do so, but to condemn men to the destruction they deserve as sinners.
This takes us through verse 18. God elects some, but not others, and He does so because He is God and He is sovereign. He can do as He chooses. Men do not deserve mercy, but God can bestow it on whomever He chooses. God would only be unjust if He withheld something from men which they had merited. No one merits His mercy. Mercy is not about us, as though we deserved it, but about God, who is gracious to men who are undeserving (see Romans 5:8).
In verse 19 another objection is raised. The argument goes something like this: “So, Paul, you are telling us that God is ultimately the one who determines our destiny, and not we ourselves (by our works). If God bestows salvation on whomever He wills, and withholds it from whomever He wills, then we mortals have no guilt, no culpability. After all, God does what He wants with men, so how can He possibly find us responsible?”
The question that is asked in verse 19 is not really answered. We shall see in chapter 10 that the Gospel must first be preached so that men may make a choice, and that the choice men make is one for which they are held accountable. But here Paul is not interested as much in the question as he is in the attitude behind it. “If being God is to be sovereign, and being sovereign means that no one should dare to question your actions (as we see in Daniel 4), then how do you dare, O man, to make accusations against God? How do you, the creature, find it permissible to question God?” God is the potter; we are the clay. God has the right to make whatever He chooses from the clay. The created being does not have the right to question the actions of the creator. As Creator, God has the right to do whatever He wishes with His creation. The potter makes some vessels for honorable uses (like Moses), and other vessels for common use (like Pharaoh). God has the right to create vessels of wrath, and also to create vessels of mercy. God’s wrath is demonstrated by means of those whom He has created for destruction; God’s mercy is demonstrated by those He has chosen to save.
If this point is true, and God, as God, has the right to choose and to reject, to create vessels of mercy and vessels of wrath, then God has the right to save some Jews, and not to save other Jews. More than this, God has the right to save as many Gentiles as He pleases.
The next verses (25-29) are Paul’s proof from the Old Testament Scriptures themselves that God had purposed from eternity past to save only a remnant of the Jews, and also those who were Gentiles. The fact that many Gentiles were coming to faith while many Jews were not is therefore the fulfillment of God’s eternal plan, and an illustration of God’s sovereignty in divine election.
Verse 30 and following leads into the next chapter. The explanation for the present state of the Jews and the Gentiles is faith. The Jews were rejected because they sought to earn salvation by works; the Gentiles were saved because they simply believed in Christ for salvation.