1) Ahijah reproaches both Solomon and Jeroboam by declaring that they will lose their kingdom and by condemning their houses. They both relate to the Deuteronomistic theology by reflecting the cycle of apostasy where the people turn away from God (in these cases by worshipping other gods) and are punished for it. Ahijah directly states that it was because the Solomon turned away from God and worshipped others in 1 Kings 11:33. God, through Ahija, does recall that He promised to never completely turn his back on David’s line (1 Kings 11:39) but He also promises to build Jeroboam a “house” in the same way He promised this to David (1 Kings 11:38).
Although it seems like the rebellion is a free act of the Israelites the fact that God takes credit for it (1 Kings 12:25) and that it is foretold as a form of divine retribution against Solomon (1 Kings 11:29-34) proves that God is responsible for the division. This however does not mean that God is to blame since this is just retribution for the people’s (general) and Solomon’s (specific) disobedience. So the division comes from an act of infidelity to the covenant but respecting it is an act of fidelity since it is the will of God. The Deuteronomistic History definitely places importance on the promise to David by making sure Ahija emphasizes that David’s house won’t be punished forever (1 Kings 11:39) so it seems as though reunification is a blessing that will come, perhaps from more obedience.
Jeroboam is to blame for establishing other centers of worship because his goal was to secure his power not to worship God (1 Kings 12:26-27). Moreover, the creation of calves seems to recall Exodus and the way the narrative states that sacrifices were made to them (1 Kings 12:32) makes this look like idolatry. Therefore Chapter 13 is fair when Jeroboam is rebuked for these centers of worship.
2) Elijah marks himself as a true prophet since what he says comes true while what the false prophets say does not come true and they are consequently put to the death as Deuteronomy 18 instructs. Just like Moses Elijah encounters God at Horeb and is hand-selected for his task, and his mission to anoint a king reflects the way Deuteronomy 17:14-20 places religious authorities above kings. While Deuteronomy 12 would seem to prohibit Elijah’s actions there is no indication of disapproval in 1 Kings 18. This seems like an instance of God working through the disorder brought about by humans to bring about order so even if it is not perfect it is preferable to allowing disorder to continue.
3) Amaziah thinks that Amos is applying to be a prophet for hire to make money for his prophecies. Amos denies being a prophet to indicate that he is not in that class of workers employed by kings. This shows that they are corrupt and perversions of the ideal of prophets, which is tobe commissioned by God directly.
The Israelites would have cheered on the condemnations of other nations since they were competitors for regional power. They would have especially been happy about the condemnation of Judah. Amos’ condemnation of Israel would have disrupted the mood of the listening Israelites. Amos points out that since God did so much from them it is all the worse that they should disobey Him (Amos 2:9-11). Israel should know better because they are the only people God knows so intimately (Amos 3:2). Amos’ prophecies represent the ideal from Deuteronomy 18 if they come true. The way Amos reminds the people of the covenant and rebukes them for disobedience also follows the general formula for all prophets. His message perfectly represents the Deuteronomic idea that disobedience causes disaster by providing a direct causal relationship between the two.
4) Hosea uses the metaphor of God as a husband to Israel as His wife. Hosea 2:4 makes Israel’s infidelity into prostitution and adultery and in response God says He will leave Israel naked (2:5) i.e. to withdraw His favor. In Hosea 2:14 God promises to destroy whatever has been given to Israel by “her lovers.” However, after a time God will try and re-attract Israel to Him (2:17) and they will be betrothed forever (2:21). Finally, God will reclaim the children of Israel whom He disowned as His own (2:25). With this understanding the deliverance from Egypt is like courtship and an alliance between Israel and Egypt or Assyria is like abandoning one’s husband for protection from another.
Compared to the way Deuteronomy and the Deuteronomic History portray the covenant this seems a lot less like a technical legal contract (although a marriage is a contract in a sense especially in these times) and more like an ongoing relationship that has problems that need to be fixed. This way perhaps makes it more relatable because marital strife is a more everyday thing than political treaties or other ways of thinking about the covenant. However, there is something odd about this language and I suppose some people would dislike the representation of gender roles with this metaphor.