The question will be answered in two parts:
A) Stripping Aisha of Her Title as the Mother of the Faithful
There is no such hadith reported in our sources in this connnection. Sa'ad bin Abdullah[1] says:  "I said to Imam Mahdi, the Imam of Time (atf)," O noble master, it has been reported from your great grandfathers that the Messenger of Allah (S) had given the authority of divorcing his wives to the Commander of the Faithful, Ali (A.S). It has even been narrated that Ali (A.S) had, in the Battle of Jamal, sent a message to Aisha telling her that she had made Islam and Muslims get bogged down in fitna (mischief) and had put her children on precipice of death. He had threatened her that if she did not regret her past actions, he would divorce her whereas, in fact, the death of the Holy Prophet (S) was a natural cause of the divorce of his wives."
The Imam of Time (atf) asked: "What does divorce mean to you?"
I said, "It means to set a woman free (so that if she wishes to marry another man, she must be free to do so)."
The Imam said: "If the demise of the Holy Prophet (S) was a cause of separation, then why was it not permissible for them to marry other men after the Prophet (S)?
I answered: "Because God, the Glorified, prohibited marriage with them after the Prophet (S)."
"How did the Prophet's demise set them free?" asked the Imam.
I answered: "O noble master, what is the meaning of the divorce which the Prophet (S) relegated to the Commander of the Faithful, Ali (A.S)?
The Imam said: "God, the Exalted, held the position of the Prophet's wives in high regard and honored them as the mothers of the faithful. The Prophet (S) also said to the Commander of the Faithful: 'O Ali, this honor will be with them as long as they obey (God) but whoever among them disobeys God and rises up against you, let her free to marry another man and get stripped of the position as the mother of the faithful."[2]
It is necessary to note that this hadith is considered to be weak due to Muhammad bin Ali bin Muhamad bin Hatam Nawfali Kirmani being in the chain of transmission. Although he is one of the masters (mashayekh) of Sheikh Saduq, according to many scholars, he is dhaif (poor). Apart from the chain of the transmission of the above tradition, there are also some points to be taken into consideration in terms of signification:
1. Considering Surah Tahrim, the title "Mother of the Faithful" cannot provide justification for all the actions done by the wives of the Holy Prophet of Islam (S).
2. Although Imam Ali (A.S) was the righteous successor of the Prophet of Islam (S) and assuming that he had the authority to do so, we could not find reliable and valid proofs to indicate that he stripped some of the wives of the Prophet (S) of their title as the mothers of the faithful. On the contrary, there are proofs showing that Ali (A.S), out of respect for the Holy Prophet (S), overlooked many mistakes committed by Aisha. Here we give a few examples:
1-2. When Ali (A.S) fought a battle against the companions of the Camel (jamal), he did not take anything as war booty. Some of his companions said: "If it is halal to fight them, then why is not permissible to take booties (spoils of war) from them, and if the booties are forbidden to take, then it is forbidden to fight them as well. Why did you fight against them without taking any captives from them?
Imam Ali (A.S) said: "Which of you is prepared to take Aisha as his share?"
Some said: "Aisha is protected from the Prophet's side and we will not take her as captive for the same reason but others are not immune and we can take them as captives…"[3]
2-2. On his way to Kufa, the Commander of the Faithful (A.S) ordered Aisha to be taken to Medina and accompanied by forty turbaned and veiled women while carrying swords with them. He ordered that Aisha be guarded from right and left; front and behind.   Aisha was complaining that Ali (A.S) had sent non-mahram men with her, thus violating the honor of the Prophet of Islam (S) but when she entered Medina and saw them (the women), she regretted what she had said about Ali (A.S). Then she said: "May Allah grant Abi Talib's son the best of rewards for respecting the Prophet (S)".[4]
B) Attributing some mean and despicable actions to Aisha after the demise of the Prophet (S)
Firstly, attributing such things to Muslims without proofs has its own specific rules one of which is that such things must be testified by four witnesses in accordance with the conditions mentioned in Shari'ah law, or else the testifiers should be punished for false imputation.
Secondly, we should speak about all Muslim women especially the wives of the Holy Prophet (S) respectfully and in a mannered manner as the Commander of the Faithful, Ali (A.S) treated Aisha in the same manner.
Thirdly, in a report by Ibn Abbas, he says about all the wives of the prophets: "Noah's wife was an unbeliever and used to tell people that her husband was mad. When someone believed in Noah and embraced his religion, she would inform the transgressors and tyrants of Noah's tribe to hurt and torment him. Noah's wife was an infidel and consented to what her tribesmen were doing ushering them to Lot's guests. This act on the part of these two women is considered to be perfidy otherwise there is no doubt that they never committed adultery and their act of betrayal was related to religion. Saddi says that their perfidy related to their being infidel.[5]

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