Solomon dies, and so his son Rehoboam takes the throne. Now Shlomo (as I like to call him) had enacted very oppressive policies, but the people thought that a regime change carried with it the hope of reform. So they approach Rehoboam and tell him, Your father made our yoke a heavy burden; but if you now lighten the harsh servitude and the burdensome yoke under which your father placed us, then we will serve you (1 Kgs 12.3).
Rehoboam does no such thing, however. He listens to the advice of his younger counselors rather than his elder counselors, and so promises the people that I will add to your yoke (v. 10). This event leads to the rupture of the Kingdom of Israel in two: ten tribes separated to form Israel, whereas Judah and Benjamin remained united to form Judah. This is a schism that would continue to exist for many years thereafter.
What is fascinating to me is the commentary of the author about Rehoboam's decision. He says: So the king did not hear the appeal of the people, because the change of mind was from the Lord, that He might establish His word which He spoke by the authority of Ahijah the Shilonite to Jeroboam the son of Nebat (v. 14). The reference is to a prophecy recorded in ch. 11: Ahijah prophesies the split of the kingdom as a punishment for Solomon's apostasy (11.27-32).
The text affirms that God brought about the change of mind in Rehoboam proximately for the sake of securing the prophecy made earlier by Ahijah, but ultimately for the sake of punishing the king for Solomon's apostasy. This might seem problematic for some persons who are convinced that God does not interfere with the freedom of will of human beings. On the contrary, the text suggests that this can happen, for example in instances of prophecy or punishment.
Now at this juncture I would like to reference a fascinating remark made by Origen in commentary on the hardening of Pharaoh's heart. Origen reasoned like this. Some persons point to that incident as evidence that human beings do not have freedom of the will. On the contrary, Origen argued, God would not have needed to harden Pharaoh's heart if he didn't have freedom of the will. If Pharaoh was intrinsically disposed to do evil, then what would be the purpose of hardening his heart? The hardening presumes that he could have relented and permitted the Hebrews to leave.
Origen's argument is interesting and there may be something to it. My own impression, reading the Old Testament, is that human beings are depicted as acting largely independently of God. Of course, there are also moments such as the incident with Rehoboam in which it would seem the Lord plays a role in the direction things take.
I am not sure what to make of this question of the relation between providence and freedom. Perhaps there is no sense in theorizing about it systematically, but rather we affirm what scripture does and use the emphases that scripture uses. Scripture certainly speaks to us in the second person as if everything depends on a choice that we must make, independently of God. Consider God's words to Israel: For why should you die, O house of Israel? For I do not will the death of the one who dies (Ezek 18.31-2). And yet, when it speaks about the choices of others in the third person, sometimes there is mention of God's intervention, "interference," etc. Perhaps that's the way we talk about things, without systematizing the matter.