Was Fatima (daughter of Prophet Muhammad) against other Caliphs (Umer, Uthman and Abobaker)? The second part of my question is why didn't Ali and Fatima want their grave to be known?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Neither Faatimah nor ‘Ali both, were in dissension against the other caliphs, namely Abu Bakr, ‘Umar and ‘Uthmaan . Faatimah died during the caliphate of Abu Bakr, so she was not alive during the caliphate of ‘Umar and ‘Uthmaan .

She was buried in Al-Baqee’ graveyard with other Companions and she never ordered to keep her grave secret. Similarly, ‘Ali did not order to keep his grave secret, as far as we know.

‘Ali married off his daughter Umm Kulthoom, may Allaah pleased with her, (whom he had from Faatimah ) to ‘Umar and ‘Ali named one of his children Abu Bakr, and he, may Allaah pleased with him, named another one ‘Umar. There are other evidences which prove that they were all brothers loving each other for the sake of Allaah The Almighty, contrary to the claims of some ignorant and sinful people who insult and blaspheme the Companions of the Prophet .

For more benefit on the relationship between Abu Bakr, ‘Umar, ‘Uthmaan, ‘Ali and Faatimah all, please refer to Fatwa 90407, and to Fatwa 91131on why Faatimah was not buried besides her father and to Fatwa ">84666, on Umm Kulthoom the wife of ‘Umar .

Allaah Knows best.