The chapter covers a long period of time, and the personages vary. The kings of north and south are powers and conflicts that swirl around the people of God sandwiched between worldly powers that seem to have all the power and might, while God's people have nothing.
From vv21-35, I interpret the northern king as Antiochus IV. Afterward, that subject is Rome. In this I agree with Calvin, though differing with him somewhat on particular detail.
The basic idea in ch.11 is that God is already aware of the events of the coming five centuries, long before they happen. Which shows that he is still in charge of history, regardless of how things look to people on the ground. The people of God will not be "in charge" of their own destiny, in earthly terms, all during this time down to the end of the Days of Indignation, v36 (which will be followed by Days of Grace). To survive, they must "hunker down," while the tides of the fortunes of Empires roll back and forth over them, and in the eyes of the world they are ignored, or despised. The secret is that God has not forgotten them, the whole time; but the world is being prepared for Messiah's arrival. Only Messiah can bring an end to the Indignation, the era that began with the Exile.
And when they do not stay humble, but seek to become more important in the world, and be "movers and shakers" (see v14 for example), this will only work against them. By creating a higher profile for the Jews, they only succeed in becoming a target for world powers like a furious and shamed Antiochus (vv32,34). Better to be a nobody on the world stage, than try to be somebody again in your own strength. God has no intention of letting them come back to strength, and certainly not while the Days of Indignation continue. The Chosen People are still under judgment, though some of them are happily permitted to return to Judah.
Ch.12 is simply the answer to ch.11. There will be days of triumph for God and his people. He will triumph over all earthly power. This chapter (like many OT Messianic texts) telescopes the first and second coming of Christ. His final triumph comes into view as that which vindicates his cause. God's people must be patient in faith and trial, until the resurrection, v2.