Duties are universally measured by relations. Is a man a father? The precept is to take care of him, to yield to him in all things, to submit when he is reproachful, when he inflicts blows. But suppose that he is a bad father. Were you then by nature made akin to a good father? No; but to a father. Does a brother wrong you? Maintain then your own position toward him, and do not examine what he is doing, but what you must do that your will shall be conformable to nature. For another will not damage you, unless you choose: but you will be damaged then when you shall think that you are damaged. In this way, then, you will discover your duty from the relation of a neighbor, from that of a citizen, from that of a general, if you are accustomed to contemplate the relations.
Duty is an important part of Stoicism, although Epictetus doesn't spend very long explaining exactly what it entails. From memory this is the clearest advice he gives. You should look to your relationship to others to determine your duty, and you should pursue that duty regardless of the quality of the person on the other side. Your duty is to be a good son, regardless of your father.
In some ways I find this advice troublesome. Relying on social norms to determine what "good" action is seems a bit risky. And to maintain a relationship with someone who damages your ablity to pursue your philosophy just because of an existing relationship seems both stupid and counter to previous advice.
What I do take away from this is that you are in control of how well you perform your duty, whatever that may be. Being a citizen of a corrupt country does not give you permission to be corrupt. If you choose to maintain a relationship (with a parent, sibling, country, boss) you should perform the duties of that relationship to the best of your ability. I should be the best employee I can be, until I am no longer an employee. The best husband I can be until I am no longer a husband. What "best" entails is highly subjective, but I think that's almost beside the point.