Is shunning one's father—due to problems arising from working with him—considered an act of disobedience and defiance, knowing that the eldest brother works independently and has no problems with their father?

If a son's independence in housing or work from his father does not diminish the father's right or fall short in honoring him, then there is no harm in it, and it is not an act of disobedience. An adult, mature son has the freedom to live independently if he is self-sufficient from his parents, but it is preferable for him not to separate from them and not to cease honoring them. Independence might be the correct path to achieve affection and avoid disputes. One must continuously honor his father and be kind to him, for his right is great, and honoring him is among the best acts of drawing closer [to Allah], as the Prophet, peace be upon him, said: "The father is the middle gate of Paradise, so if you wish, squander this gate, or preserve it."