What is the ruling on going to crowded, mixed-gender markets when compelled by one's mother, and what are the consequences of that?

You must accompany your mother to the market if she asks you, unless your going out results in disobedience [to God], and you must lower your gaze from forbidden things.

You should gently advise your mother to reduce her visits to the market unless there is a necessity, because it is the most hateful of places to Allah, and her going out should be modest and in accordance with Islamic guidelines.

It is not permissible for you to abandon your mother or disobey her command unless she orders you to commit a sin. You must treat her well and advise her gently and wisely if she violates the Sharia, and you should strive to guide your family towards obedience to Allah, as Allah the Almighty says: "O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones."