Is it considered disobedience for children to sit in their rooms instead of sitting with their father in the living room, especially if his presence leads to problems and heated discussions, and is accompanied by the father's criticisms of them in front of relatives?

There is no harm in staying in your room to avoid hearing your parents' arguments and problems, especially if your presence escalates the discussion or angers your father. This is not an act of disobedience; rather, it is the better course of action with this intention. We advise you to be dutiful and kind to your parents, and to be patient with your father and speak gently to him, in obedience to the Almighty's saying: "And your Lord has decreed that you not worship except Him, and to parents, good treatment. Whether one or both of them reach old age [while] with you, say not to them [even] 'uff,' and do not repel them but speak to them a noble word. And lower to them the wing of humility out of mercy and say, 'My Lord, have mercy upon them as they nurtured me when I was small.'"