Selling share of house?

This just will not work. You can only give any one person 3k a year. Anything over that and you are disposing of assets. Your mums assets are obviously below IHT level though so tax is not the issue. When her assets go above a set level she has to fund her own care, if she cannot because she disposed of her assets by gift to you or your brother, then her family would be held liable for the payments. As your brother is a minority share holder in the property a court could, and in the circumstances probably would, order the sale despite his opposition.