Is Mu'awiyah ibn Abi Sufyan's rejection of Ali ibn Abi Talib's order to dismiss him considered a sin against the ولي الأمر (Wali al-Amr - rightful ruler), and what is the clarification of the Great Fitna (sedition)?

It is not established that Ali (may Allah be pleased with him) dismissed Mu'awiya (may Allah be pleased with him) and that Mu'awiya refused. One must refrain from discussing the disputes that occurred between the Companions and instead propagate their virtues. The bloodshed that took place between them is not included in the warning, "If two Muslims meet with their swords, then the killer and the killed are in the Hellfire." The doctrine of the Ahl al-Sunnah (People of the Sunnah) is to have a good opinion of them, and to interpret their fighting as a result of their ijtihad (independent reasoning) and ta'wil (interpretation), not intending disobedience. Rather, each party believed they were in the right. And a mujtahid (one who performs ijtihad) who errs incurs no sin. It is not permissible to attribute certain error to any of them, for they are imams, and we have been commanded to refrain from discussing their disputes and to mention them only with the best of mentions.