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.
If the situation is as you mentioned in the question that you believed that the time of the prayer was over, and you delayed the prayer due to your mother wanting to relieve herself, then we hope that you are not sinful because you believed that you had to make up the prayer because its time was over.
Even according to the view that one is obliged to immediately make up a missed prayer, as per the opinion of the Hanbali and Maaliki School, then it is permissible to delay making up a missed prayer if there is a sound religious reason, as stated by the Hanbali School. Allowing your mother to enter the toilets before you is a sound reason, Allaah willing.
Moreover, Allaah will not hold into account the Muslim Nation for things they commit by mistake, or things which they forget, or which they were forced to do.
However, you should try to wake up early in the future in order to perform the Fajr prayer at its prescribed fixed time and with the congregation in the mosque if possible.