2 Kings 9: 8 tell us that "The whole house of Ahab will perish." In chapter 10 we are told that Jehu did all that the Lord "had in mind to do." If the whole house of Ahab was killed, then how is Joash, son of Ahaziah, still alive if Ahaziah is related to Ahab by the marriage of his father Jehoram to Athaliah (8:18)? Would he not be included as a member of the "house of Ahab," which would mean he should be dead by this point? I'm reading through Kings for the first time, so I am unaware of what happens to Joash after chapter 11.
Here are some brief facts:
- Omri founded a new dynasty for the northern kingdom of Israel after killing Tibni
- His son Ahab was the second king of this "Omride" dynasty and ruled for 22 years
- The third king was Ahaziah who ruled for 2 years
- The fourth and last king was Joram who ruled for 12 years
- Jehu assassinated Joram and established a new dynasty. Jehu ruled for 27 years.
As @Lucian has correctly pointed out (comment above):
A man fathers his own house; he does not become part of the house of his father-in-law. He is part of his father's house, but certainly not of his father-in-law's.
There is another similar situation with the wife:
for women, marriage means moving from the authority of her father's house to that of her husband's house.
Thus, it becomes quite clear that neither Jehu, the king of the northern kingdom of Israel, and Jehu's parents, were never part of the house of Ahab - Jehu founded a new dynasty in the northern kingdom