Is it permissible to give the obligatory charity (Zakat) for the repentant female borrower to her mother, knowing that the mother will spend it on the necessities of the family and the borrower's needy siblings, in the event that it is impossible to return the money to its original owners?

Whoever repents from infringing upon the rights of others, their accountability is not cleared until they return the rights to their owners or seek their forgiveness. If they are unable to reach them, they should give that money in charity on their behalf with the intention of reward for them. If the owner of the right appears later, inform them of what you have done. If they approve, then all is well; otherwise, you must pay them their right, and the reward for the charity will be yours. It is permissible to give this money to your poor and needy relatives, provided that their maintenance is not obligatory upon you, and on the condition that you do not favor them over someone who is more in need.