Is it permissible for me to live with my brother in one dwelling, knowing that my wife lives with us, and my parents insist on that despite my fear of falling into an unlawful seclusion (khalwa)?

It is not permissible for you to allow your brother to live in your house in a way that leads to him entering upon your wife and secluding himself with her in your absence. This is forbidden, due to the Prophet's (peace be upon him) saying: "No man should seclude himself with a woman unless a mahram is present." There is no disobedience to your parents in this, because obedience is only in what is good, and "there is no obedience to a creature in disobedience to Allah Almighty." You should convince your brother of this and seek his help in convincing your parents. It is a sign of noble character to invite your brother to the house when you are present.