You say that The property was owned by your father against a sale deed by seller on stamp paper. That means, in the Revenue Records, the property is in your father's name.
Simply my mutating your and your mother's name (that too by getting only simple affidavit from your brother) in the Municipal Committee records, the property cannot be said to be only in your and your mother's name.
Legally speaking, all the three of you i.e. your mother, you and your brother are even today equal share holders in the property.
Therefore, if you desire that the entire property is to come to you, then your mother and your brother have to execute a Registered Relinquishment Deed relinlquishing their share in the property in favour of you. With the Registered Relinquishment Deed (which involves very very nominal stamp paper) the entire property cannot come to your single name. (Thereafter, on the basis of the Registered Relinquishment Deeds, you can get the mutation of your name alone in the Municipal Committee records).
Whenever you propose to sell the property, then apart from the Sale Deed in favour of your father, you have to always have the Registered Relinquishment Deed given by your mother and your brother with you. Then and then only you will be able to successfully sell the property.
You were thinking about the Gift Deed from your mother. That is a very costly idea as in that case heavy Stamp Duty on the value of the share of your mother in the property has to be paid. That is a wasteful expenditure, which can be avoided by adopting the Relinquishment Deed procedure.
