What should I do about my promise to my maid for an 'Umrah after two years, knowing that she cannot travel long distances by car, and I cannot afford a plane ticket?

You are not required to do anything. As long as you intended to fulfill the promise, but she does not want to travel by car, and you cannot do otherwise, there is no blame upon you. Fulfilling a promise is recommended by the majority of scholars, not obligatory. One who neglects it misses out on virtue and commits a gravely disliked act, but does not incur sin.