Did Muawiya or his son Yazid kill Hasan by persuading one of his wives to administer poison?

When Hasan lay on his deathbed, his brother Husayn asked him:
"Brother, tell me who is the one who poisoned you."
Hasan asked: "Why? That you may kill him?"
Husayn said: "Yes," to which Hasan responded: "I will not tell you anything. If it is the one I think it is, then Allah's revenge is harsher. And if it is not he, then by Allah, no innocent person will be killed on account of me." (Ibn Kathir, al-Bidayah wa al-Nihayah vol. 7 p. 41; al-Dhahabi, Siyar A'lam al-Nubala' vol. 3 p. 273; al-Mizzi, Tahdhib al-Kamal vol. 6 p. 251; Ibn hajar, al-Isabah vol. 2 p. 13; Ibn Abd al-Barr, al-Istiab vol. 1 p. 390)

This authentic narration shows Hasan was not sure of the culprit and refused to tell his brother whom he suspected, fearing he might be accusing an innocent person.

The only report in which Mu'awiyah is implicated in the death of Hasan is narrated by the historian Muhammed ibn Umar al-Waqidi:
I heard some people saying Muawiya secretly made one of his servants administer poison to him.

As a report of history, this narration suffers from two serious defects. The first is the universally recognised untrustworthiness of al-Waqidi about whom Al-Shafii said:
In Madinah there were seven people who used to forge chains of narration. One of them was al-Waqidi

Secondly, al-Waqidi does not cite the narrators. Coming after other reports where he mentions names of narrators this adds further doubt about this report.

In another report the wife of Hasan, Jadah bint al-Ashath, is asked by Yazid ibn Mu'awiyah to do it, promising to marry her. It is reproduced by al-Mizzi in Tahdhib al-Kamal as follows, finding its way into the history books:
Muhammed ibn Salam al-Jumahi narrates on the authority of Ibn Judubah that Jadah, the daughter of Ashath ibn Qays, was the wife of Hasan ibn Ali. A message was sent to her in secret by Yazid, telling her: "Poison Hasan and I will be your husband." So she did it. When Hasan died she sent a message to Yazid asking him to fulfil his pledge. But he told her: "By Allah, we did not approve of you as Hasan's wife. Shall we approve of you as our own wife?"

Yazid ibn Iyad ibn Judubah lived in Madinah during the time of Imam Malik. Imam Malik's student, Abd al-Rahman ibn al-Qasim, once asked his opinion about a person called Ibn Saman.
Imam Malik replied: "He is a liar."
Ibn al-Qasim then asked: "And Ibn Judubah?"
Imam Malik replied: "An even bigger liar, an even bigger liar."
All other rijal critics who ever expressed themselves on his status as a narrator have concurred with Imam Malik in some way or the other.