My mother invites my family to eat on Thanksgiven day after her guess are gone because she doesn't want to waste the food. Is it permissable for my family to go to her home or eat the food left from her dinner?
That is permissible, because food is respectable and pure, and that is better than throwing it away. It is permissible to eat the food of the Christians because Allaah says (interpretation of the meaning):
“The food (slaughtered cattle, eatable animals) of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them”
So there is nothing wrong with that. Their bread, their food, and whatever dishes and sweets etc they cook are all good and pure, and there is nothing wrong with them. But if the food has been made for that celebration, it is not permissible to be there at the time of the party, but after the party it is permissible to eat the food and that is better than throwing it away.