What is the ruling of Islamic law regarding someone who swore, "By Allah, I will not have relations with you tonight," then proceeded to do so, and offered an expiation for the oath as a donation to a post office that serves widows?

If the oath was merely a slip of the tongue and not intended as a binding oath, then it is considered a 'laghw' (idle) oath, for which there is no expiation, in accordance with Allah's saying: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what your hearts have earned [of intention]," and His saying: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what you intended of oaths."

However, if the oath was intended as a binding oath, then expiation is obligatory. What your father donated to a project does not waive the expiation, because Allah has specified its recipients in His saying: "So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or freeing a slave. But whoever finds not [the means] - then a fast of three days." Therefore, it is obligatory to give the expiation again as stated in the verse.