Does a person sin if he asks his mother, who believes it is permissible to uncover the face and hands, to bring him something from the market, whether she is going to the market at his request or not?

There is no harm for your mother in uncovering her face and hands in front of non-mahram men, as long as she follows the opinion of the Maliki school, which does not obligate covering them, and this opinion is widespread in your country. There is no harm for you in going with her to the market or asking her to bring something from it, but this must be done in a polite and respectful manner befitting filial piety.