Is the incident of Fatimah complaining about Ali, and the Prophet, peace and blessings be upon him, saying to her: "By the Lord of the Kaaba! Return to Ali and tell him that you are willing to rub your nose in the dust to make him happy; let him do as he pleases," authentic or fabricated?

There is no narration about Fatima, may Allah be pleased with her, complaining about her husband Ali, may Allah be pleased with him. As for a wife complaining about her husband, some complaints are legislated to avert harm, such as Hind bint Utbah’s complaint to the Messenger of Allah, peace be upon him, about Abu Sufyan's stinginess. Some complaints are for seeking advice and avoiding discord, such as Fatima’s complaint, may Allah be pleased with her, about Ali’s proposal to the daughter of Abu Jahl. As for problems that can be solved through dialogue and patience, it is better not to complain about them, unless there is a need for the advice of a wise third party. It is preferable that problems between spouses be solved with wisdom and good manners.