Is it permissible to give zakat to sisters living with their wealthy mother who receives rent exceeding the household expenses, and to aunts of moderate means, based on a fatwa that considers it both charity (sadaqah) and upholding kinship ties (silat ar-rahim)?

You erred in appointing your mother as an agent to distribute the Zakat (definition), because an agent does not have the right to appoint another agent unless authorized by the principal, and this is the most preponderant opinion. You must inform the owner of the money about what happened. If he does not approve of your action, then you are liable for the money and must return it to him or spend it as he instructed. If he approves of your action, then if your mother placed the money in its rightful place, it is permissible; otherwise, she is liable for it. Your paternal aunts and sisters are not eligible to receive Zakat.