That being said, I can understand that now that his son is gone, there is a lot of grief (afterall, now it's final. There will never be reconciliation), and attending a funeral (which is for the living I believe) brings closure for some. I can see why he thought he would go, even if I can understand why Cory's mom wouldn't have invited him.
As you said, the funeral is for the living. I know and have discussed with my DH that, if he passed before his cut off parents, I would not invite them to his funeral. The exact same actions and personality traits that led to them being cut off would also lead to them causing problems and more pain for the people who loved DH and would be at the funeral by virtue of the fact that they were close to him in life. In my opinion, the grief and comfort of the people close to the deceased in life takes precedence.
So it's possibly this actor's mother, or other relatives, did not invite the father not because of his rel*ationship with his son, but his rel*ationship or the way he would act around the mourners.