OP, it wasn't over Christmas, but my mother once invited herself to a very meaningful, once in a lifetime, and extremely traumatic event, to stay with us. I had never once told my 'mother' no.
But I took one look at my poor, nigh on broken, husband and children's faces when they heard the news, and rang my mother up, and said, 'I'm really sorry, but we can't have you here for this, you are not invited, and you are sadly not welcome, for this time.'
Fall out? Boy howdy, the tears, the anger, the histrionics, and then, the silence. Two blessed weeks of silence when she wasn't talking to me. After that, because I'd been unmovable, she rang, and said she'd decided 'this had gone on long enough'. I think she realised that she was gonna have to do the ringing, because for once, I wasn't going to do the crumbling and crawling.
Now, she's a bit more used to the notion that she needs to ask, rather than demand, because a 'no' is more than a theoretical possibility. Go for it. Seize the fish? What is the worst, really, that can happen?
If the palpitations, vapours, tears and smelling salts fail to impress, what is the worst they can do?
Or alternatively, do what my sister did with her husband, who actively seeks to make Christmas miserable for everyone, tell him exactly what it is that he does that pisses you off, and tell them they are on notice NOT to do that this Christmas, or it will be cut short, and be the last Christmas you host them. And mean it.