Praise be to Allaah.
Shaving the head or cutting the hair is one of the obligatory
duties of ‘Umrah, and the one who forgets it should do it when he remembers.
If he did any of the things that are forbidden when in ihraam before that,
out of ignorance or because he forgot, then he does not have to do anything,
according to the most correct scholarly opinion.
Based on that, your wife has to cut her hair now, and thus
she will exit ihraam from her ‘Umrah, and she does not have to do anything
because of the intercourse that took place, because she only did that
because she thought that she had exited ihraam following ‘Umrah.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said
concerning a woman who did not complete her ‘Umrah:
With regard to the things she did that are haraam when in
ihraam, let us assume that her husband had intercourse with her at this
time, and intercourse when in ihraam is the most serious of the forbidden
things. But she does not have to offer any fidyah because she was unaware
(of the ruling). Every person who does one of the things that are forbidden
in ihraam out of ignorance or because he forgot or was forced to do it, does
not have to do anything (i.e., offer any fidyah).
From Majmoo’ Fataawa Ibn
Some scholars are of the view that having intercourse after
doing saa’i and before shaving the head or cutting the hair means that the
fidyah is required, even if one forgot or was unaware of the ruling, but it
is fidyah in the sense of being optional, like the fidyah offered in the
event of an ailment in the scalp, i.e., the fidyah for one who shaves his
head because of an ailment such as lice and the like, as is indicated by the
words of Allaah (interpretation of the meaning):
“And whosoever of you is ill or has an ailment in his
scalp (necessitating shaving), he must pay a Fidyah (ransom) of either
observing Sawm (fasts) (three days) or giving Sadaqah (charity — feeding six
poor persons) or offering sacrifice (one sheep)”
So he should fast for three days, or feed six poor persons by
giving each one of them half a saa’ of wheat or other staple food, or
slaughter a sheep to be distributed among the poor of the Haram (in
See: Sharh Muntaha al-Iraadaat (1/556).
Your wife may follow this view so as to be on the safe side,
so she may fast for three days or feed six poor persons or slaughter a sheep
to be given to the poor of the Haram.
And Allaah knows best.