Firstly: 

The noble Sahaabi Mu‘aawiyah (may Allah be pleased with him) was one of the scribes who wrote down the Revelation; he was well known for forbearance, knowledge and virtue, and his achievements and good characteristics were many. And it is not permissible to cast aspersions upon him at all. He was one of the leaders of the Muslims who ruled on the basis of justice as much as he could. With regard to what happened during his time of turmoil and internal conflict, we should refrain from discussing it and should not talk about it on the basis of falsehood. We testify that all the Companions of the Messenger of Allah (blessings and peace of Allah be upon him) were good and virtuous; whoever among them tried to work things out and got it right will have a twofold reward, and whoever among them tried to work things out and got it wrong will have one reward. 

Please see the answer to question no. 140984 

Secondly: 

When ‘Ali (may Allah be pleased with him) died, and his son al-Hasan (may Allah be pleased with him) offered the funeral prayer for him, the people swore allegiance to him as caliph, and they urged him to mobilise to fight the people of Syria. He had no intention of fighting anyone, but they prevailed upon him and gathered a huge number of men, the like of which had never been seen before. He marched with the army, heading towards Syria, then turmoil, differences of opinion and division arose in the army. When al-Hasan ibn ‘Ali realised that the army was not all united behind him, he resented them and at that point he wrote to Mu‘aawiyah ibn Abi Sufyaan (may Allah be pleased with him), offering to come to terms for a peace deal between them. Mu‘aawiyah sent ‘Abdullah ibn ‘Aamir and ‘Abd ar-Rahmaan ibn Samurah to him and a peace deal was concluded. Al-Hasan swore allegiance to Mu‘aawiyah as caliph, and yielded the caliphate to him. That occurred in 40 AH, which was called the year of unity (‘aam al-jamaa‘ah) because the people united under Mu‘aawiyah in that year.

The Messenger of Allah (blessings and peace of Allah be upon him) foretold this action and praised al-Hasan for it, namely giving up leadership and no longer seeking it, thus sparing the Muslims from bloodshed and seeking that which is with Allah. So al-Hasan gave up the caliphate and passed the reins to Mu‘aawiyah in order to unite the Muslims behind one ruler. 

Al-Bukhaari (2704) narrated that Abu Bakrah said: I saw the Messenger of Allah (blessings and peace of Allah be upon him) on the minbar, with al-Hasan ibn ‘Ali beside him, and he turned to the people sometimes and turned to al-Hasan sometimes, and said: “This son of mine will be a leader, and perhaps Allah will bring about reconciliation through him between two great groups of Muslims.” 

When Mu‘aawiyah seized power and entered Kufah, he gave a speech there and all the people throughout the regions were united behind him. al-Hasan ibn ‘Ali, along with his brother al-Husayn, the rest of their siblings and their cousin ‘Abdullah ibn Ja‘far, travelled from Iraq to al-Madinah al-Munawwarah – blessings and peace be upon the best of its inhabitants. 

When Mu‘aawiyah was dying, he summoned Yazeed and gave his final instructions to him, and the people swore allegiance to Yazeed. Among them were many of the Sahaabah, including Ibn ‘Umar and Ibn ‘Abbaas (may Allah be pleased with them). al-Husayn ibn ‘Ali and ‘Abdullah ibn az-Zubayr (may Allah be pleased with them) refused to swear allegiance to him. 

See: al-Bidaayah wa’n-Nihaayah (8/16-21 and 8/175). 

Ibn Battaal (may Allah have mercy on him) said: 

Al-Hasan handed over the reins of power to Mu‘aawiyah, reconciled with him and swore allegiance to him, pledging to listen and obey so long as he ruled according to the Book of Allah and the Sunnah of His Prophet. Then they entered Kufah and Mu‘aawiyah received the oath of allegiance from the people of Iraq. That was the year of unity, when the people united and came to an agreement, and war ceased. All the Sahaabah who had stayed away from civil war swore allegiance to Mu‘aawiyah. Sa‘d ibn Abi Waqqaas, ‘Abdullah ibn ‘Umar and Muhammad ibn Muslimah swore allegiance to him, and the people were very happy about that. Mu‘aawiyah bestowed upon al-Hasan ibn ‘Ali three hundred thousand dinars, a thousand garments, thirty slaves and one hundred camels, and al-Hasan ibn Ali left for Madinah. Mu‘aawiyah appointed al-Mugheerah ibn Shu‘bah as governor of Kufah, and he appointed ‘Abdullah ibn ‘Aamir as governor of Basrah, and he left for Damascus, which he took as the capital of his kingdom. 

End quote from Sharh Saheeh al-Bukhaari (8/97) 

Thirdly: 

The scholars stated that al-Hasan ibn ‘Ali stipulated that Mu‘aawiyah should not appoint anyone as his successor; rather the matter was to be decided by consultation among the Muslims. 

Ibn Hajar al-Haytami (may Allah have mercy on him) said: 

When they reconciled, al-Hasan wrote it in a document to Mu‘aawiyah, as follows: 

In the name of Allah, the Most Gracious, the Most Merciful. This is what has been agreed upon by al-Hasan ibn ‘Ali (may Allah be pleased with him) and Mu‘aawiyah ibn Abi Sufyaan. He has made a peace deal with him on the basis that al-Hasan will hand to him the reins of power to rule the Muslims, provided that he rule according to the Book of Allah, may He be exalted, the Sunnah of the Messenger of Allah (blessings and peace of Allah be upon him) and the way of the Rightly-Guided Caliphs. Mu‘aawiyah ibn Abi Sufyaan has no right to appoint anyone to succeed him; rather the matter is to be decided by the Muslims on the basis of consultation and shoora. [This agreement is also] provided that the people should be safe wherever they may be on Allah’s earth, whether they be in Syria, Iraq, the Hijaz or Yemen; and provided that the companions and party of ‘Ali should be safe, and their lives, property, womenfolk and children should be safe wherever they may be. Mu‘aawiyah ibn Abi Sufyaan gives his solemn promise and oath before Allah to that effect, and that he intends no ill towards al-Hasan ibn ‘Ali or towards his brother al-Husayn, or any of the members of the family of the Messenger of Allah, either secretly or openly, and he will never disturb any of them, no matter where they may be. 

This was witnessed by So-and-so, and by So-and-so the son of So-and-so, and sufficient is Allah as witness. 

When the peace deal was done, Mu‘aawiyah requested al-Hasan to speak before a gathering of people and tell them that he had sworn allegiance to Mu‘aawiyah and handed over the reins of power to him, and he agreed to do that. 

End quote from as-Sawaa’iq al-Muhriqah ‘ala Ahl ar-Rafd wa’d-Dalaal wa’z-Zandaqah (2/399) 

See also the book al-Hasan ibn ‘Ali (may Allah be pleased with him) by Dr as-Sallaabi (p. 253) [This book is available in English under the title Al-Hasan ibn ‘Ali ibn Abi Tâlib: His Life and Times]. 

Fourthly: 

When Mu‘aawiyah (may Allah be pleased with him) saw the extent of the dissent, division and turmoil among the people, and the extent to which they were prone to internal conflict, he feared that their division might become worse after he died, and that dissent and turmoil would increase. So he decided that the best solution was to take allegiance for his son after him. He consulted the senior Sahaabah, the leaders of the people and the governors of the regions, and they all give their consent to that. Delegations came agreeing to swear allegiance to Yazeed, and many of the Sahaabah also swore allegiance to him, to the extent that al-Haafiz ‘Abd al-Ghani al-Maqdisi said: His caliphate was valid; sixty of the companions of the Messenger of Allah (blessings and peace of Allah be upon him) including Ibn ‘Umar, swore allegiance to him. It is proven in Saheeh al-Bukhaari (7111) that Ibn ‘Umar swore allegiance to Yazeed. It was narrated that Naafi‘ said: When the people of Madinah announced that they no longer accepted Yazeed ibn Mu‘aawiyah as caliph, Ibn ‘Umar gathered his close friends and children and said: I heard the Prophet (blessings and peace of Allah be upon him) say: “A banner will be set up for every betrayer on the Day of Resurrection.” We swore allegiance to this man in accordance with the conditions enjoined by Allah and His Messenger, and I do not know of any betrayal greater than that of one who swears allegiance to a man according to the conditions enjoined by Allah and His Messenger, then begins to fight him. If I ever learn that any of you withdrew his allegiance or gave allegiance to someone else, then that will mark the end of the relationship between me and him. 

Perhaps the reason why Mu‘aawiyah told the people to swear allegiance to Yazeed was that he thought that this would prevent division and would unite the people at that critical stage through which the ummah was going, as he was aware that many people were claiming the right to be the caliph. So he (may Allah be pleased with him) thought that appointing Yazeed as caliph was in the best interests of the ummah and was a precaution that would prevent turmoil, if the decision-makers agreed on him. 

See: al-Mufassal fi’r-Radd ‘ala Shubahaat A‘da’ al-Islam (13/228) 

Ibn Khaldoon (may Allah have mercy on him) said: 

What prompted Mu‘aawiyah to give precedence to his son Yazeed and appoint him as caliph, rather than anyone else, was the belief that this would serve the interests of the Muslims by uniting them and bringing them together behind one man, with the approval of the decision-makers at that time, who were from Banu Umayyah, because at that time Banu Umayyah would not accept anyone (as caliph) except one of their own number. They were the strongest clan of Quraysh and the ones who had the greatest influence. So Mu‘aawiyah preferred Yazeed, over others who may have been thought more qualified than him, for that reason, and he overlooked others who were more virtuous in favour of one who was less virtuous, because he was keen to keep the Muslims united behind one leader, which is a matter of great importance in Islamic teachings. It is not possible to think of any other motive for Mu‘aawiyah than that, because his good character and the fact that he was a Sahaabi would rule out any other motive. 

The fact that some of the senior Sahaabah were present and kept quiet indicates that there was nothing suspicious in what Mu‘aawiyah did, because such people would not be deterred from speaking out against something wrong, and Mu‘aawiyah was not one of those who would be too arrogant to accept the word of truth. All of them were too noble to do that, and their good character would rule it out. 

End quote from Muqaddimat Ibn Khaldoon (p. 109) 

He also said: 

Mu‘aawiyah issued instructions for Yazeed to become caliph for fear of the Muslims becoming divided. 

End quote from Muqaddimat Ibn Khaldoon (p. 106) 

Muhibb ad-Deen al-Khateeb (may Allah have mercy on him) said in his commentary on al-‘Awaasim min al-Qawaasim (p. 229): 

Mu‘aawiyah did not choose the best option because he was afraid of turmoil and bloodshed if he left the matter to shoora (mutual consultation). He thought that strength, obedience, order and stability would be on the side of those who supported his son (i.e., they had more power and would be more able to maintain order). End quote. 

In conclusion, Mu‘aawiyah (may Allah be pleased with him) did what he thought best served the interests of the ummah at a time of division, when there was turmoil in its ranks, and he thought that keeping the Muslims united and warding off turmoil was more important than fulfilling the condition stipulated by al-Hasan (may Allah be pleased with him), when he gave up his claim to the caliphate and swore allegiance to him. Sharee‘ah seeks to attain and perfect that which serves the people’s best interests and to ward off and reduce that which causes harm. 

Moreover, the most that can be said concerning this matter is that Mu‘aawiyah (may Allah be pleased with him), who was the caliph of the Muslims, tried to work out what was the best option concerning this issue. He would have two rewards if he got it right, and he would have one reward if he got it wrong, in sha Allah. What happened in this case or others of imperfection or shortcomings on his part may well be overlooked and forgiven by the Most Gracious, Most Merciful, and the Companions of the Prophet (blessings and peace of Allah be upon him) are more deserving of being excused and pardoned by Allah, may He be glorified and exalted. 

And Allah knows best.