All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
One’s abstinence from whatever may break the fast starts by any of the two incidents:
Firstly, being sure of the break of true dawn, whose light spreads evidently throughout the horizon.
Secondly, hearing a trustworthy Mu'dhin who is well aware of the prayer times.
If your wife was not able to verify whether or not she ate the pre-dawn meals after the appearance of the Fajr time or after she heard the Adhan of the Fajr prayer by someone whom she trusts, as mentioned, then her fast is valid and enough for making up for the days that she missed in Ramadan. This is because validity is the original case of her fasting, and this validity should not be changed except due to a reason that does not lack certainty. Your wife’s mere doubt about the validity of her fasting should not be considered. If she is certain that she ate the predawn meals after the time for Fajr time had come or after she had heard the Adhan for the Fajr by a trustworthy Mu'dhin, then her fast is invalid and she is required to fast two days instead of the two days of which her fast was invalidated.
Allaah Knows best.