You, your sister and your mother have the right of inheritance as the first legal heirs. If your father's parents are alive, they are also the first legal heirs (legal heirs: spouse, children, parents).
If your mother wants to sell this house alone, you need your brother and sister and your father's parents (if they are still alive) to give up the inheritance in writing, and your father's death certificate issued by the hospital (which is safer) to be notarized by the local notary office. If not, go to the court for mediation or judgment of inheritance, then go to the Housing Authority for transfer procedures, write down your mother's name, and then sell it and transfer it to someone else's name. As for the specific cost of consulting the real estate trading center, notary fees and the like will be collected by notary agencies.