All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
At first, you are not allowed to spoil your wife's fast since she is making up for the missed days of Ramadan, which is not permitted to be violated because it is an obligation for the person who starts it.
As for you, there is no blame on you because your fast is supererogatory and one who observes optional fast is allowed to break his fast when he likes, especially if one breaks it for a sound Islamic reason.
With regard to making up for spoiling the optional fast, then this is not required. As for a person (like your wife) whose fast is spoiled, she has to make up for the missed day since her fast was obligatory, in addition, she has to seek Allah's Pardon.
Allah knows best.