All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, you should know that it is not permissible to accuse your mother of stealing and of deceiving you; this consists in serious undutifulness. What is even more sinful and serious is to announce this and talk about this with people. Therefore, you must sincerely repent, apologize to your mother and try to satisfy her so that she forgives you. You should never do anything that would harm her as she is the most worthy person of your good companionship, and if someone is not kind to his mother, who carried him in her womb with hardship and gave birth to him with hardship, then it is even less likely he will be kind to anyone else.
You should know that the mother has the right for her children to provide for her if she is in need; and if she is well off, then she has the right to be comforted and treated charitably, as well as to be treated with kindness and dutifulness and to receive good relations. It is also permissible for the mother to take some of her children's money and use it without excess and without causing harm to them. Please refer to Fatwa 89942.
As regards your brother, he is not entitled to take your money, but since he has admitted to taking it, as you mentioned, then you have the right to demand that he returns the money he has taken from you.
For more benefit, please refer to Fatwa 92038
Allaah Knows best.