It is implied that the 'Iron Law' is the law of the 4 corners yet Its not in Vintas? or it is?

The Iron Law of Atur is a holdover from the days of the empire. It persists in Atur, Vintas, and the Commonwealth. The major inovation of the sturan Empire was tying the legal system to the church, which contributed to both surviving its collapse.

The jurisdiction of the Iron Law isn't entirely clear, but it seems to cover the major crimes against the person, heresies, and retains the authority to resolve provincial civil cases.

I'm generally confused about the government in the 4 corners. Who rules the Commonwealth?

The governing body of the Commonwealth is in Tarbean. It's most likely a house of lords acting in their own interests.

Is Atur still the center of government (where king Robert sits?) with subjugated governorships essentially?

Atur is in decline. It's a feudal monarchy with a king in the capital. Roderic Calanthis is the king of Vintas, which is also pretty much a feudal monarchy.

Ceald and Modeg appear to be monarchies as well. The text notes that they both have monarchs.

The region is a pastiche of legal systems. The Commonwealth has a common law system similar to England in the 1500s that overlaps with the Iron Law. Local nobles apparently have some individual discretion within their own lands.

The Cealdish control international trade and currency exchange and weild the economic and political power to punish folks attempting to work outside the system.

And there's quite a bit of townsfolk barely giving a second thought to any of that, particularly when the town is pretty far from the action.

So, yah, it's difficult to understand because some thought went into making the Four Corners reasonably diverse.