Is it permissible for a Muslim woman to eat a small amount of vegetables cooked on top of non-halal meat to avoid arousing her mother's suspicions?

The animal slaughtered by a person from the People of the Book is permissible, provided that no name other than Allah's was mentioned. However, the animal slaughtered by an idolater or an atheist is not permissible. Pork is also forbidden. Anything cooked with forbidden meat is likewise forbidden due to its impurity. You are not permitted to eat what is forbidden except out of necessity. If your family discovering your conversion to Islam would result in severe harm, such as death or imprisonment, then there is no blame in eating from forbidden food for fear of your matter being discovered, as Allah the Almighty says: ﴿He has only forbidden to you dead animals, blood, the flesh of swine, and that which has been dedicated to other than Allah. But whoever is forced [by necessity], neither desiring [it] nor transgressing [its limit], there is no sin upon him. Indeed, Allah is Forgiving and Merciful.﴾