Is expiation incumbent upon one whose mother swore that he would not accompany her as her mahram, knowing that he had already sworn to do so?

It would have been better for you to fulfill your oath and accompany your mother. Since that did not happen, you have broken your oath, and you owe an expiation for breaking an oath. This expiation is: feeding ten poor persons, or clothing them, or emancipating a slave. If you cannot find any of these, then you must fast for three days. This is if your oath was intended as a self-imposed obligation to travel with your mother. However, if it was intended as a gesture of honor towards her, then there is a difference of opinion regarding the necessity of expiation for you, and the preponderant view is that expiation is not obligatory.