It doesn't sound like anyone actually eats Christmas dinner with gran?
The OP is kind enough to drop off some food, and other relatives visit her... but it reads as if she's on her own for her actual Christmas meal, which sounds a bit sad for an 86-year-old with so much family.
Can't another solution be found where she gets to spend her Christmas meal with people?
I completely understand why the OP can't have gran round at hers (the toilet issue is real!), and if gran lives on her own, she probably can't accommodate the OP, her OH and the kids. There's only so much squishing together of people you can do in a one-bed property. Possibly the other relatives have the same issue with too many people to cram in or don't live close enough for the logistics to work.
It sounds a lot like the OP's parents should be taking gran out, as if it's just the two of them to organise.
So... I understand why the OP is so frustrated. They are the most obvious solution and they don't seem to care.
OP, does your mum not get on with gran?
Your aunt doesn't offer to cook - does she normally eat a traditional Christmas dinner at home? If so, she might not offer, but could she be asked?
I think you need to insist another relative takes responsibility, and separately (they don't need to know this), you make arrangements to visit your gran for a proper chinwag on a less stressful day for you (Boxing Day? the day after?) so you are still spending time together.
Could your OH be the person who contacts the family to insist on another solution? He may be less likely to cave to pressure/emotional blackmail.