What is the ruling on taking government-provided psychiatric medications not intended for sale, obtained through a hospital employee, with the knowledge and permission of the director?

If the manager is authorized to dispense medications, then there is no harm in you taking them from your sister's husband. However, if he is not authorized, then it is not permissible to take them, and your sister's husband must return them to the workplace; because that is a breach of trust, as Allah Almighty says: "O you who have believed, do not betray Allah and the Messenger or betray your trusts while you know [the consequence]." (Quran 8:27), and as the Prophet, peace and blessings be upon him, said: "On the hand is what it took until it fulfills it."