Dear Hadi,
Dear Reader,
Thank you for your question. Our opinion, and God knows best, is that yes, if you are leading your wife in prayer and you make a mistake, she can correct you. Let's take a closer look.
With regards to alerting the imam in prayer to a mistake, the Prophet (pbuh) said that men should say subhanAllah and women should clap (Sahih al-Bukhari).
You have probably been in congregational prayers where if the imam makes a mistaken, men following him will frequently do more than just say subhanAllah. Specifically, they will often recite a relevant word or two of the mistaken verse to both alert and assist the imam in correcting the error. The hadith noted above does not describe this specific approach to correcting the imam, but it has become a commonplace method used. We believe this has occured because this hadith falls more in the category of a hadith about etiquette (rather than jurisprudentially binding) i.e. it is recommending an appropriate way to alert the imam to a mistake, but perhaps is not the only appropriate way in which this can be done.
Regardless of this variation, the hadith clearly indicates a manner in which women following the imam in prayer can alert the imam to a mistake - traditionally by lightly clapping. That being said, because we think this hadith is one of etiquette rather than binding practice, we believe, and God knows best, that if you and your wife are the only two praying and you make a mistake, there is nothing inappropriate in her correcting you by reciting one or two words of the relevant verse that was mistakenly spoken.
In peace.