How should I handle a sum of money given to me as a reward from government funds, in exchange for personal work I performed for the head of the authority and his wife?

Public funds are a trust that must be safeguarded, and betraying them is forbidden. One form of betrayal is using them for unauthorized personal purposes. Therefore, if it is highly probable that the money you were rewarded with originated from public funds, it is impermissible to take it, and the perpetrator of this evil must be prohibited from doing so.