Is it permissible for my mother to give my brother ownership of my bedroom furniture without my consent?

Your mother does not have the right to give your furniture to your brother without your consent. If you do not consent, you are not considered disobedient, and we hope that her prayer against you will not be answered in this case, because a parent's prayer against their child is only effective if the child has wronged them. However, we advise you to let her dispose of the furniture if you do not need its monetary value, in order to avoid her anger and to purify your intention for the sake of Allah, seeking reward. For honoring one's parents is among the best deeds, and patience in doing so is a cause for Allah's pleasure.