answering the question, Sheikh Ahmad Kutty, A Senior Lecturer and an Islamic Scholar at the Islamic Institute of Toronto, Ontario, Canada , states,

I pray that Allah enhances our love for Islam and help us remain steadfast.
as for the questions, regarding attending funeral and dinner of non Muslim parents:
1. You can attend the funeral of your relatives or friends; this includes the rituals of cremation and the associated rituals, as long as you are not administering the rites. The Companions of the Prophet (peace be upon him) attended the funerals of their dead relatives who were non-Muslims.
2. You may also partake of the meals prepared by your parents or relatives. It does not matter that the food is cooked in the same oven.
3. You may also sit in the same table with your parents who may consume alcohol as long as you do not consume it.