Hadith e Kissa which says that the Prophet(pbuh) brought Imam Ali, Hassan, Hussain and Lady Fatima under the cloak and said "O Allah, they are people of my house and remove from them evil and purify them a perfect purification" is a very famous and authentic hadith.
This hadith is also written in Sahih Muslim narrated by Aisha.
In the narration of Trimdhi, we can clearly read that the Holy Prophet(pbuh) did not allow Umme Salma(one of the righteous wife of the Prophet) to join them under the cloak.
It proves that those Ahlulbayt are the special specific people for whom this verse revealed where the Holy Prophet announced "O Allah these are my Ahlulbayt".
For more details please read our article "Who are the Ahlulbayt - Are the wives of the Prophet part of ahlulbait".
The narartions of Trimdhi clearly prove that The Holy Prophet (pbuh) told his wife Umm e Salma that you have your own status which is good. But you can't join these people for whom I am going to announce the verse of purification (Ayah Tatheer).
English Translation:
Sayyidah Umm Salamah (RA) reported that when thisverse was revealed (O Ahlulbayt Allah wants you to take away the impurity from you). Then the Prophet (SAW) called Hasan, Husayn, Ali and Fatimah in Umme Salma's house and he put the cloak on them then prayed,
“O Allah, they are people of my house and remove from them evil and purify them a perfect purification.”
Then Umm Salma (RA) asked "Am I not with them?"
The Prophet said, “You are on your place and you are on good".
Here is another narration
English Translation:
Sayyidah Umm Salamah (RA) reported that the Prophet (SAW) put a cloak over Hasan, Husayn, Ali and Fatimah and prayed,
“O Allah, they are people of my house and closes to me. Remove from them evil and purify them a perfect purification.”
Umm Salamah (RA) submitted, “I too am with them, O Messenger of Allah!”
He said, “Indeed you are on what is good.”
