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.
It is forbidden in Islamic legislation to perform open supererogatory prayers (i.e. prayers that are not performed for any specific reason, like the two Rak'ahs upon entering the mosque) during these times, i.e. at sun rise and at sunset, and after ‘Asr until sunset. As regards when there is a reason for performing the prayer, like the prayer of salutation to the mosque, the two Rak’ahs after Tawaaf, it is permissible to perform them during the time of prohibition according to the predominant view of the scholars.
For more benefit in this regard, please refer to Fatwa 84280.
So, if this woman and her son perform open supererogatory prayers during these times, then you are obliged to advise her and rebuke her with wisdom and good and soft words. Whoever fulfills the obligation of advising is not sinful. However, one should not despair and stop advising as long as it is expected to benefit.
Allaah Knows best.