The descendants of each of Jacob’s 12 sons had become a **tribe** or very large family group in the nation of Israel. Everyone in Israel belonged to one of the 12 tribes.
This could mean ‘refused to follow Rehoboam as their king.’ It might help to start this sentence with ‘So’ or ‘Because of that’ or ‘Because of what Rehoboam said.’
This is not possession, but it gives the name of the kingdom. It could be translated as: “the Judah kingdom.” (See: [[rc://en/ta/man/translate/figs-possession]])