Sorry for being prickly. This will be the first time in 3 years that mum is well enough to attempt a family Christmas, we've all been excited to be together and SIL has tarnished it with her antics.
So sorry to read this. You sound very balanced and reasonable. When elderly parents reach this stage of their life one always has the 'this could be the final Christmas together' thought lurking in the back of one's mind.
I'm reminded of my own mother's situation when she had cancer and was in her final year. Three of her generation of relatives refused to see her, even for her last Christmas, once it was clear she was dying. My guess is they were living in fear or denial of their own mortality and wanted to pretend that death wasn't going to happen to them. My mum, who was an absolute darling and anxious to make the most of what time she had left, was very hurt and couldn't understand why she was being shunned by people she'd always felt close to.
I wonder if your SIL has MH issues around illness and disability and mortality? I don't think it's that unusual, sadly. What's her relationship like with her own mother? I think I might send her a message in a couple of days that reflects how deeply hurt you are by her behaviour. Something like this, perhaps:
'I feel the need to tell you, SIL, how hurt I am by your suggestion that I should cancel my own mother's invitation to spend Christmas with my family. This will be the first time in three years that she has been well enough to attempt a family Christmas and we've all been excited at the thought of being together. We're not going to allow you to tarnish what will be a lovely time for us. In the new year you and I need to get together so that you can explain your extraordinary demand in a way that I will be able to understand and perhaps forgive.'
I hope you, your parents, your MIL and the rest of your family all have a lovely time together.