Is a wife rewarded for completing a recitation of the Qur'an by listening to her husband's recitation in Qiyam prayer, or must she recite it herself to obtain the full reward?

The reward for the listener is not the same as the reward for the reader. The difference between them depends on the level of devotion (khushu'), contemplation (tadabbur), and adherence to the proper manners. It is sunnah to listen to the recitation to share in the reciter's reward. The congregant (ma'mum) is commanded to listen attentively to the imam's recitation when he recites, based on Allah's saying: "And when the Qur'an is recited, then listen to it and pay attention that you may receive mercy."