Am I obliged to fulfill my oath not to contact my wife for three weeks as punishment for her disregard of my oath, or is that considered a dereliction of my duty as a husband and father, knowing that I do not absent myself from her for more than five months?

You should know that frequent swearing is something we have been forbidden from. It is better for a man to be patient with his family's character and not to hasten to anger. We advise you to resume contact with your family and expiate your oath, for the Prophet, peace and blessings be upon him, said: "Whoever takes an oath and then sees something else as better than it, let him do that which is better and expiate his oath." You should also inform your wife of the obligation for her to obey you in what is good and reasonable, and this includes responding to your requests for her to answer your calls.