What is the ruling on a mother taking her grandmother's pension to care for her and for a sick uncle, with the knowledge of the entire family, but without the grandmother and uncle knowing the actual amount of the pension, and with the grandmother forgiving the mother? And does the ruling on this money transfer to the children if the mother gives them some of it or buys something for them with it?

It is not permissible for the mother to take her mother's money without her knowledge and consent. A general request for forgiveness is not sufficient if the grandmother is of sound mind. However, if she lacks the capacity to dispose of her wealth, then it is not valid for her to gift her money. As for what the mother spends on her mother and brother, if it was a donation, there is no returning it. If she intended to be repaid, she is only entitled to what she spent. It is not lawful for you to take money that your mother gave you from your grandmother's money, which she took without her knowledge and consent. However, if she spent on you from her commingled wealth, the preponderant opinion is that it is permissible for you to benefit from it, especially if the majority of her wealth is lawful.