In this chapter, Rehoboam becomes a vassal of Shishak as punishment for abandoning the Law of Moses.
This chapter covers a single sequence of events, the invasion of Judah by the Egyptians, but in this single event we can see several important themes of Chronicles emerge. I will cover these themes in turn.
First, this chapter shows the decline of Judah, which is signified by the loss of the golden shields of Solomon (v. 9). It says in v. 10 that Rehoboam replaced them with bronze shields, replacing the gold with a less valuable material. This is a material representation of Judah's declining influence and wealth. Their declining prosperity is directly linked to their moral decline (v. 1-2), but through the intermediary role of the Egyptians as conquerors.
Since gold is associated with the holy place and bronze is associated with the courtyard, we can symbolically interpret this as Rehoboam (or the kingship as an institution) being driven out of the holy place and into the courtyard as a punishment for Rehoboam's sin. The fact that Rehoboam can make the bronze shields (and remain in the symbolic courtyard) is because of his repentance.
I think it is a tremendous irony that because Rehoboam became "established" and strong, he and Judah slid into idolatry. The Chronicler is basically saying that Rehoboam's sin is pride, and it's a pride that comes from his strength and security. Establishing that strength and security was the topic of the previous chapter, which is perhaps why the Chronicler spent so much time discussing the fortified cities and other details of Rehoboam's reign. The irony is that Judah's strength only comes from their previous obedience to the LORD. David had great victories over his enemies because he was faithful to God, and Solomon had great wealth because of David's victories, and now Rehoboam has great security and strength because of what Solomon built, and this is exactly why Rehoboam and the people with him begin to abandon the LORD. The lesson here is that in many cases, the blessing that comes from God can lead people into pride which takes us away from God who gave us the blessing in the first place. Biblically, material blessings can be a very dangerous thing, particularly in the Old Testament. There are a handful of men who handle it well (Abraham and David) and many who do not (such as Rehoboam).
Second, this chapter shows that after Judah sinned, they were judged, but after they repented, God showed forgiveness. This is an application of the first principle in God's declaration to Solomon. Similar to Deuteronomy 28, it shows that sin and obedience to God have direct consequences in God's treatment of Israel/Judah.
Third, in this chapter the "evil mother" theme emerges. There is a broad (but non-universal) pattern of evil kings in Judah typically having evil mothers. Most of these mothers are marked as evil for either being non-Israelite (as in this case, v. 13) or being from the house of Ahab (that had their own idolatry problem). Even the house of Ahab had their own "evil mother", in Ahab's wife, the non-Israelite Jezebel. I think there are a few things worth saying about this theme.
First, Exodus 34:12-16 condemns marriages between Israelites and the native peoples of the land. This is something I discussed before with respect to Solomon, who also had many foreign wives (1 Kings 11), and in Kings this was given as the reason why the kingdom was taken away from Solomon's descendants. Moreover, in Numbers 25 we are told that Israelite men had "sexual immorality with Moabite women, who invited them to the sacrifices to their gods." This draws a very strong association between Israelite men having relations with non-Israelite women, and being subsequently drawn into idolatry as suggested by those women.
Second, while some people may think of this as a blind and perhaps even racist proscription, I think the repetition of this pattern shows that there is a definite reality here. Many people in ancient Israel did intermarry with the native tribes and were drawn into syncretism or idolatry as a result. In the Chronicler's time, this is perhaps an even more urgent issue because the Assyrians and Babylonians had resettled lots of foreigners into Israel and Judah respectively, so it was very important that Judah avoid mixing together with these foreigners to maintain their distinctive culture and faith. Otherwise, their devotion to the LORD would have definitely been compromised.
Third, I think this theme is a fascinating exposition of the power dynamics between men and women in ancient Judah. There are a lot of people who believe the bible is highly patriarchal, and I think there's a lot of truth to that, but I think this theme shows that while the role of women in the bible can be subdued, women are nonetheless highly influential in Chronicles. As we see, it is usually not the quality of the father that determines the character of their successor, but the quality of the mother. There are a lot of righteous kings who had evil successors (David to Solomon to Rehoboam is one example, a crisper example is Manasseh, an evil son of the righteous Hezekiah). However, as a general rule any time Chronicles mentions any queen by name, if that queen is evil then her son is evil and if that queen is righteous then her son is also righteous. In that sense, it is the women of the royal household who dictated the future of the nation, because the men they raised up to be kings would in turn have so much influence over the nation's faith.
That concludes my discussion for this chapter. In the next chapter, Rehoboam's son Abijah defeats Jeroboam in battle.