Is a mother permitted to prevent her daughter from observing a voluntary fast, claiming she needs food, and is the daughter allowed to fast in this situation without her mother's consent?

Parents can prevent their child from volunteering for Hajj, fasting, jihad, and other similar acts, especially if they believe it would harm him or if their needs cannot be met without his presence. As for obligatory duties (fara'id), he cannot be prevented from them. If a child is prevented from a voluntary act by his parents, his reward is with Allah.