Is expiation incumbent upon one who swore to her mother-in-law that she would not take money out of her purse to pay, while she did take out the money and gave it to her husband, who then paid, knowing that the one who swore did not intend a vain oath?

Your mother-in-law should have responded to your request and fulfilled your oath. If she did not, then an expiation for breaking an oath is incumbent upon you, which is feeding ten poor persons, or clothing them, or freeing a slave. If you cannot find any of these, then fast three days. This is if your oath was intended to obligate her. However, if it was intended as a gesture of honor, then the predominant opinion is that no expiation is required.