Is it permissible for a Muslim to eat meat prepared by his non-Muslim mother from a non-halal store, and what is the ruling on refusing this meal?

If the method of slaughter used by a People of the Book is unknown, and the prevalent method in their country is stunning or slaughtering for other than Allah, then their slaughtered meat is not permissible to eat. Eating is also prohibited if game meat becomes mixed with dogs on which the name of Allah was not mentioned, or if it falls into water, because doubt concerning the lawful slaughter (dhakāt shar‘īyah) renders it forbidden. If the mother brings impermissible meat, it is not permissible to eat it, due to Allah’s saying: "Forbidden to you are carrion" (Quran 5:3). One must be gentle when explaining the reason for abstaining.