There is much too little information given here to give you an appropriate answer. To actually transfer the home your mother could simply have a deed prepared and transfer the house from herself to you. This could be very inexpensive but I would advise hiring an attorney to prepare the deed. The problem is that we have no idea about your mother's estate plan or goals or why she wants to do this. Also, if the house is transferred to you, as the recipient of the gift you could have a large tax issue if and when you sell the house when compared to receiving the house via her estate.
The bottom line is that you and your mother (and it sounds like your brother) all need to visit with an estate (elder law, special needs) attorney to assess the full scope of the situation so that a big mistake is not made that has long-lasting effects.
This is not legal advice nor intended to create an attorney-client relationship.
I agree with the other contributor. You should seek advice from an estate planning/ elder law attorney that can give your mother advice based on her situation taking into account tax issues and long term care needs.