Praise be to Allah.
Firstly: the woman in ihram is not allowed to wear the niqaab because the Prophet (blessings and peace of Allah be upon him) said: “The woman in ihram should not wear niqaab or gloves.”
This has been discussed previously in the answer to question no. 12516.
Secondly: the prohibition on a woman wearing niqaab whilst in ihram does not mean that she should leave her face uncovered in the presence of non-mahram men; rather she must cover her face with something other than the niqaab or burqa‘.
The Prophet (blessings and peace of Allah be upon him) did not instruct the woman in ihram to uncover her face; rather he told her not to wear the niqaab. There is a difference between the two matters; she should not wear the niqaab but she should cover her face with something other than the niqaab, such as the scarf.
It was narrated that ‘Aa’ishah (may Allah be pleased with her) said: The riders used to pass us when we were with the Messenger of Allah (blessings and peace of Allah be upon him) in ihram. When they drew close to us, one of us would let down her jilbaab from her head over her face, and when they had passed us we would uncover it again.
Narrated by Ahmad, 23501; Abu Dawood, 1833; classed as hasan by al-Albaani.
Shaykh al-Islam (Ibn Taymiyah) said: She may cover her face and her hands, but without wearing the garment that is made to fit that part, just as a man is not allowed to wear trousers but he may wear the izaar (waist wrapper).
End quote. Majmoo‘ al-Fataawa, 22/120
This issue has been discussed previously in the answer to question no. 120377
Thirdly: even though it was a mistake to uncover the face after entering ihram, the ‘umrah is not affected by a woman uncovering her face after entering ihram or whilst circumambulating the Ka‘bah (tawaaf) or going between as-Safa and al-Marwah (sa‘i). The ‘umrah is valid and we hope that it will be accepted in sha Allah, especially since your wife uncovered her face due to lack of knowledge of the Islamic ruling.
And Allah knows best.