OP, it seems to me that other posters have made very good suggestions for an economical solution to your side dish and meat/main course issue, or for communicating your concerns to family members.
I could be wrong, but I'm sensing the real issue here is the manner in which you were "invited" to the event in the first place. Here, I quote: "Apparently we (that is the family as a whole, including the extended cousins and what not) are funding this whole thing. We weren't asked, oh no. We were ordered. My Aunt (mom's sister) called her tonight, and was contacted by Cousin J. Cousin J is the daughter of the Great Aunt who is dying."
From the way you describe it, I could understand if you feel like you and your mother were dictated to by a bossy relative, and as a result, perhaps feel a bit annoyed. It's much more pleasant to be consulted rather than "ordered" to do something.
Since this event is being held for the purposes of spending time with a terminally ill relative, I would urge you to try to be as patient and understanding as you can with your cousin, who is the daughter of your dying Great Aunt. I know from sad experience that people who are in grief during the final stages of a loved one's illness are under a great deal of stress and other strong emotions. Therefore, they might not be as polite or patient as they normally would be. People in grief sometimes act very out of character and say and do things they usually wouldn't. In fact, your cousin might be under a great deal of pressure trying to pull together rather large event in a short time frame, while trying to attend to the needs of her mother and having to deal with her own emotions at the same time - in addition to her usual responsibilities and daily life.
So, I think it would be appropriate to cut her a little slack right now. I would encourage you to take a deep breath and help your mother put together an inexpensive plate of food (the suggestions on here are wonderful) and go. Don't let the food issue ruin possibly the last time you and your mother get to see your relative.
If there is just no possible way you can manage to put together a plate of food, I'm sure your family will not hold it against you. It seems to me the point of this event is not so much about food, but rather saying goodbye to a family member. So, on that basis, I would either try to put something modest together as a gesture, or just explain the circumstances to your aunt or cousin who is arranging this and offer to bring something less expensive (maybe a liter-size bottled soft drink? Or some store bought potato salad? Perhaps a large bag of potato chips?) or just go and don't worry about the food. Given the situation, the family may not even care if you don't bring anything.
However, if you think doing any of these things would cause a lot of drama and tension, or if the food issue is a huge deal breaker, or if you feel resentful or annoyed, perhaps its best if you don't go. It wouldn't do to inadvertently add tension to a situation that is already painful.
***edited by mr kitty for content***