All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad (
) is His Slave and Messenger.
We thank you for your concern in protecting your mother from falling into what is unlawful.
Know that a mother has an immense right over her child. Allah, the Most High, has commanded excellence toward parents. However, this does not mean remaining silent and refraining from advising her. Rather, you should exert whatever reasonable means you can to rescue her from the situation she is in. This, in fact, is a form of dutifulness and kindness toward her. However, you must choose effective and gentle methods in your advice, and Allah will record for you great reward for doing so.
If she responds, then that is good. If she does not, then you have fulfilled your duty. Nevertheless, you should not completely cease advising her from time to time.
Similarly, if you advise her and she does not respond, then there is no sin upon you in accompanying her to public places if you are unable to prevent her from going out without wearing hijab.
Lastly, even more appropriate than that is accompanying her during travel, even if the travel coincides with virtuous days such as the first ten days of Dhul-Hijjah, because traveling alone is prohibited for a woman according to the majority of jurists.
Allah Knows best