Omitted second tashahhud by mistake

The scholars differed concerning the ruling on sending
blessings upon the Prophet (peace and blessings of Allaah be upon him)
in the tashahhud. The Hanbalis are of the view that sending blessings upon
the Prophet (peace and blessings of Allaah be upon him) is an essential
part of the prayer. The Shaafa’is are of the view that it is obligatory –
and this was also narrated in one report from Ahmad. The Hanafis and
Maalikis are of the view that it is Sunnah. 

There is no sound, clear evidence to indicate that sending
blessings upon the Prophet (peace and blessings of Allaah be upon him)
in the tashahhud is an essential part of the prayer. The hadeeth of Abu
Mas’ood al-Ansaari, in which he says: “Allaah has commanded us to send
blessings upon you, O Messenger of Allaah; how should we send blessings upon
you?” (narrated by Muslim, 405) does not prove that it is obligatory to send
blessings upon the Prophet (peace and blessings of Allaah be upon him)
in the tashahhud, because they were asking him how; they were no asking him
how to do that in the prayer. 

Hence evidence that it is Sunnah to send blessings upon the
Prophet (peace and blessings of Allaah be upon him) in the tashahhud is
derived from the marfoo’ hadeeth of Abu Hurayrah: “When any one of you
finishes the last tashahhud, let him seek refuge in Allaah from four things:
from the torment of Hell, from the torment of the grave, from the trials of
life and death, and from the evil of the Dajjaal.” Narrated by Muslim, 588. 

Based on the above, the most that can be said about what this woman omitted from her prayer is that it is obligatory, although the view that it is Sunnah is a strong view. But because she caught up with the whole prayer with the imam, the imam bears responsibility for her shortcoming. And Allaah knows best.