Is a father to be obeyed when he gives his son the choice between severing ties with his brother or with him, due to an inability to resolve a major dispute between the father and the eldest son?

What is obligatory upon you is to be dutiful to your father and to maintain ties with your brother. If you can maintain ties with your brother without your father's knowledge, then that is what is obligatory. However, if you cannot combine maintaining ties with your brother and gaining your father's رضا (satisfaction), then you are not obligated to obey your father in this matter, because obedience is only in what is right (ma'ruf). You must be dutiful to your father and strive to please him, and endeavor to reconcile between him and your brother. For obedience to parents is obligatory in what is right, and maintaining ties of kinship is also obligatory. And there is no obedience to a creature in disobedience to the Creator.