Is the son obligated to obey his father and agree to marry the sister of another person in exchange for that person marrying his own sister, knowing that non-compliance will lead to the father's anger and displeasure?

Obeying one's father is obligatory unless it involves disobedience [to Allah]. The Lord's pleasure is found in the father's pleasure. If the son fears falling into haram due to delaying marriage, then he must marry after advising his father gently, while alerting the father to the danger of marrying off his female ward without a dowry, which is known as Shighar.