You have already read the dispute between Zain ul Abideen, the grandson of Ali, and Muhammad bin hanafiyah, the son of Ali on imamate.
There is a long tradition in Al Kafi, about the burial of the mother of Ali ibn Abi Talib, the Prophet (s) is attributed of saying:
فإنها سئلت عن ربها فقالت وسئلت عن رسولها فأجابت وسئلت عن وليها وإمامها فارتج عليها، فقلت: ابنك، ابنك [ابنك]
Than she was asked abut God, which she told, than she was asked about the Messenger , which she answered, than she was asked about the wali and Imam, on which she kept silent , than I said to her : Your son, Your son [Your son]
Apparently this doesn’t seem like something big, but if you notice, she answered who her God is, who her Messenger is, and she forgot the Imamate and wilayah of her son? She was unaware of the Imamah and wilayah of Ali till death? What can be the reason? Lets start speculations like the Shiites.