Yes, it is permitted for your wife to take a haircut if that is what she usually does before she goes sot the Mikvah.
Explanation:
The prohibition not to get a haircut during Sefirat Haomer is because of Aveilut, mourning, for the students for R’ Akiva who dies between Peach to Shavuot. (The Maharal writes that the decree was only until Lag BaOmer but anyone who became ill before Lag BaOmer died afterwards until Shavuot. The hint to this is the gematria of Kavod (the y dint’ act with Kavod to each other) is 32, that he decrees was only 32 days.)
In the Hilchot of Aveilut the Shulchan Aruch (YOD 390:5) and the Rema argue if she can get a haircut:
Shulchan Aruch says that woman is permitted to take a haircut after Shiva. The Rema is stringent.
The base of the argument depends on a statement in Masechta Smachot (7:11): (An Avel is forbidden to take a haircut) How? He is forbidden to remove hair either on his head or his moustache, his beard, or any hair, just as he is forbidden to cut any hair after Shiva.
The Gra adds in the words, a woman is permitted to cut hair after Shiva, and he is …
The Rif and Rambam take the Beraita at face value that women are permitted to take haircut after Shiva.
The Ramban (Torat Ha’adam) I understand that is only referring removing unwanted facial hair (The Prisha understood he meant all body hair.)
The Gra understood that the disagreement was whether it is permitted for women to remove hair is by hair on the head or body hair.
The Shulchan Aruch is lenient that woman can cut her hair after Shiva and of course so too Sefirat Haomer which is less stringent. A woman has no prohibition take a haircut during Sefira. (R’ Ben Tziyon Abba Shaul Or Letziyon 3:17:3, R’ Ovadia Yosef Chazon Ovadia Yom Tov pg. 261).
Even according to the Rema, the Poskim disagree by the Omer.
The Panim Meirot (3:37) writes a woman is permitted to take a haircut during the nine days, since even by Aveilut the Rif and Rambam say she can get a haircut after Shiva and especially by the nine days one can follow the lenient opinion by a Rabbinic ordinance.
R Moshe Feinstein (IM YOD 2:137) writes that even though the basic halacha is to be lenient by Sefirat Haomer it is good to try to be stringent if there is no need to get a haircut.
In our situation that is something she usually does for Leil Tevillah even according to the Rema it would be permitted. (So ruled R’ Shlomo Zalman Auerbach and Rav S. Wosner.)
