How did Al-Hasan and Al-Husayn (may Allah be pleased with them) die, and did Yazid play a role in their killing?

Al-Hasan and Al-Husayn, the sons of Ali and grandsons of the Messenger of Allah, peace and blessings be upon him, are from the Household of Prophethood. We love and are loyal to them. It has not been proven that Yazid ordered the killing of Al-Husayn or rejoiced at it. Rather, he was ordered to prevent Al-Husayn and deter him from his course, and the killing was carried out by Ubayd Allah ibn Ziyad. As for Al-Hasan, it is well-known that he died from poisoning, and it was said that his wife, Ja'dah bint Al-Ash'ath, poisoned him. It was also said that this was at the instigation of Yazid or Mu'awiyah, but these statements are not authentic and nothing from them is proven. The most probable explanation is that he died a natural death.