It was Mu'awiya's ardent desire to impose his son Yazid (who had been named after his uncle) upon the Muslims by making him the succeeding Khalifa, despite the fact that Yazid was the playboy of the time, with many evil habits including gambling, heavy drinking, and indulgence in the pleasures of the flesh.
But the peace agreement would not permit Mu'awiya to appoint Yazid as his successor, (According to the agreement Imam Hassan would immediately become Khalifa upon Mu'awiya's death). Therefore, it was obvious to Mu'awiya that, if Al-Hassan did not outlive him, Mu'awiya could do as he pleased. Thus Mu'awiya planned to kill Imam Al-Hassan in order to pave the way for his son Yazid to be his successor.
Mu'awiya sent one of his agents to contact Imam Al-Hassan's wife Joda who was the daughter of Al-Ash'ath (once a secret agent for Mu'awiya against Imam Ali in the Battle of Siffin). Joda was asked a small favor, i.e., to put a little poison in Al-Hassan's food, and in return Mu'awiya would give her a large sum of money and also make her wife of his son Yazid. She found the offer too attractive to ignore, and foolishly agreed to accept it.
A few days later, she mixed poison in honey and gave it to the Imam. As soon as the Imam took the poisoned honey he became seriously ill. Sensing that his death was imminent, the Imam designated his brother Al-Hussein (AS) to be the third Imam. Although Imam Al-Hassan knew he was poisoned, he did not reveal that to anyone but to his brother Al-Hussein.
One thing Al-Hassan had wished was to have his burial by the side of his grandfather, Prophet Muhammad (pbuh). Imam Hussein made all the arrangements to fulfill that wish but Mu'awiya's governor over Medina did not let that happen and used military force to stop it. Imam Al-Hassan was 47 year old when he died of poisoning.
Medina was never the same without Imam Hassan (AS). Everyone missed him dearly. People at first did not believe Mu'awiya poisoned Imam Al-Hassan, but soon found out the truth.
When Hussein (AS) was designated as the 3rd Imam he was 46 years old. Imam Hussein (AS) carried on with his mission of teaching Islam as before. A large number of people kept coming to see him and to learn from him. This process continued for several years when people began to hear an ugly rumor that Mu'awiya wanted his son, Yazid, to succeed him.