Is it permissible for my mother to take money from the funds of the "jam'iyyah" (cooperative/association) that she manages when needed, provided she commits to repaying the amount to its owners on time?

There is no objection to the agreed-upon "staff association" for each member to pay a monthly sum in rotation.

However, it is not permissible for the person in charge of the association (the treasurer) to take anything from its funds for their own needs, even if they intend to return it. This is because it is a disposition of funds without permission, and it is considered a breach of trust and an encroachment on the money of others. A trustworthy agent does not dispose of what they are entrusted with except with the permission of the delegator.