It's a shame that Christmas will be 'different' for the vast majority this year.
However, the people for whom it's going to be hardest are the ones who have lost loved ones this year (to Covid or anything else).
Your DD is 11, old enough to understand why your Mum doesn't want to risk getting it.
Why on Earth do you 'disagree' with your Mum protecting herself? Forming a bubble with you (an hour & a half away) means she can't fit a bubble with people that live closer to her, so thsts not the best option for her AND it's not going to stop her getting it - it's not a magic force field.
You can have a lovely Christmas with DD if you put your mind to it. Spend time together in the run up making & baking. Plan what you two would like to eat for Christmas Dinner. Go through the radio times (when it comes out) and pick out the films you want to see. Buy a new game you'll both enjoy.
'No room' at your siblings is rubbish. When I was a kid we used to have aunts, uncles,cousins staying, always at least 13 of us in a 3 bed semi with 1 bathroom. (grandparents used to sensibly stay home & come over in the morning!). I'm sure your siblings have enough floor space for an air bed - but maybe they're being sensible & sticking to just their immediate family too.
I'm going to be spending Christmas on my own this year, so I'm not coming from a position of family smugness. But as long as all my loved ones are well, I'm fine with that.