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.
The jurists differed in opinion about a person who paid the Zakat but it was lost before reaching the people who are entitled for it, whether or not such a person is acquitted (from paying it again). The view we adopt in Islamweb is that it is better for a person in such a case to pay the Zakat again in order to be on the safe side and to be acquitted from it.
Therefore, your mother should pay the Zakat for the second time.
If your brother who lost his bag was not negligent, he is not responsible for the lost money but if the money was lost due to his negligence, then in this case he is responsible for the lost money.
The jurists stated that the agent is not responsible for the money he lost if he is not negligent and he should be believed without having to make an oath, unless the case is brought before th e court. If the case is brought before the court, his statement that he was not negligent is accepted, and he would have to make an oath to this effect.
Allaah Knows best.