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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First of all, you should know that in principle a woman should stand behind men when she prays with them. Imaam Muslim reported that the Prophet led Anas, and his mother or his maternal aunt in prayer. Anas stood on the right side of the Prophet while the woman stood behind them. [Muslim] So it is disliked for a woman to stand in front of men in a congregational prayer except in case of a necessity [for example like in the Haram Mosque [Makkah] where it is absolutely impossible to separate men from women in prayer].
In case the woman prays in front of men in congregational prayer, her prayer is valid according to the opinion of the majority of the jurists of the four schools. Therefore, your mother is not obliged to make up that prayer.
Allaah Knows best.