OP I sympathise and I think you are getting a hard time on here.
I've only read the first 7 pages so I'm sorry if I've lost the drift of the discussion.
People (yesterday anyway) seemed to be missing the point; you are being leaned on to facilitate everyone else having the perfect Christmas Day, not just once, but every year. Your gran is your (dad's/mum's) first responsibility. You've got your own family and children to prioritise. What if you announced you were all going out to a restaurant?
PPs are picking on you because plating up a meal and driving it to someone doesn't sound too much - but it's Christmas Day (I know how much that would put me out if we were all trying to get Christmas Dinner co-ordinated). I'd rather have an extra guest than have to get into the car and drive an hour round-trip - and let's face it, you couldn't just throw it at your gran and run - it would work out being much more than an hour. I appreciate, from reading your post, that inviting her over isn't an option due to her mobility issues.
The baddies here, it seems to me, are your parents first and then your siblings for not taking turns. But I really think your parents should have arranged their meal out either to include your gran, or to give them time to drop her meal off first (old people often prefer to eat earlier in my experience).
It's really unfair, but my advice would be: grin and bear it this year (or you'll feel awful) but put your foot down big-time for next year AND TELL THEM NOW. I think your parents need telling that their mum (sorry - don't know whose) is THEIR reponsibility - you've got your own family. They need to take this on board from the afternoon of Christmas Day...plenty of warning.
Yes, I feel sorry for you gran - but I'm not blaming you, OP - you're the only one who's actually doing anything for her!