Sometimes we need to pick a hill to die on, OP, and this one is yours.
“No Mum, I don’t want to change the arrangements we’ve already made.”
“No Mum, my friends don’t want to come to your house, they were invited to mine.”
“No Mum, it doesn’t suit me to cook at yours this year.”
“No Mum, I won’t be coming, but you’re very welcome to come to me, as we originally planned.”
Ad nauseum.
As everyone else has said, you need to assert yourself. This isn’t about Christmas dinner. Your mum is manipulative and controlling and used to having her own way, and it sounds like you’ve allowed her to walk all over you for a very long time.
But you’re grown up now. You have your own life. She doesn’t get to tell you how to live it. Read up on FOG as others have suggested, and give yourself some strategies for dealing with what will undoubtedly be a stressful and difficult conversation. She won’t like it, but once you realise you can set your own boundaries and THERE IS NOTHING SHE CAN DO ABOUT IT, trust me, it will feel unbelievably liberating.
Think of it like toilet training a puppy. It’s a bit of a struggle and not pleasant for either of you, but as long as you’re consistent she’ll eventually get used to it! Good luck 