Must a woman be accompanied by a mahram when she goes to work? And what is the ruling on a mother refusing her son's presence with her in the car, claiming that she is not in seclusion with the driver? And is she sinful for that?

A woman is not required to have a mahram (unmarriageable kin) when going out for purposes other than travel. As for riding alone with a non-mahram driver, some scholars have prohibited it, considering it to fall under the forbidden khalwa (private seclusion), while others have permitted it if there is no fear of fitna (temptation or discord). If your mother follows the opinion that permits it, then there is no harm upon her if she is safe from fitna, and there is no sin upon you for not going out with her. However, if there is a fear of fitna, then it is not permissible for you to leave her alone with the driver, and her anger with you will not harm you. The great right of the mother must be observed, and she must not be mistreated.