In Obadiah, Edom is called the house of which brother of Jacob?

Answer: Esau

Obadiah speaks of Esau being pillaged and condemns Edom for violence against "your brother Jacob."

“But how Esau will be pillaged, his hidden treasures sought out! Because of the violence against your brother Jacob, you will be covered with shame and cut off forever.”— Obadiah 1:6, 1:10 (BSB)