I'm sorry to be harsh but too bad for your parents. Maybe your girls will decide they want to do alternate Christmases from now on. They and you need to accept and respect your daughters choice here (NOT agree with it - it is not a democracy, they don't need you to agree nor do they need your parents to agree).
"Should" your girls spend Christmas with you and them. I think absolutely. I would be terribly hurt too.
But you can't control them.
I think you have it arse-about. Christmas is not your big issue. Your big issue is how to help nurture a better relationship with your girls.
Tell them you'd love to spend some time over Christmas with them whenever they are free. Leave the door open. Welcome them in. If you can't be flexible then it is what it is. Why do you expect them to bend to your inflexibility?
In case you haven't noticed I am projecting massively here.
I have another side to this. My father was a POS addict who we left when I was 10 and he OD'd when I was 17 with some horrible, nasty violent stuff before and after we left him. She didn't tell me any of it. I saw it with my own eyes. She never said a bad word about him (except for the rare outbursts of 'you are just like your father!' which still sting to this day).
My mum raised my sister and I all by herself on the smell of an oily rag with ZERO support from family or friends. I mean nobody.
She sacrificed. She did without. She had no life for herself. She worked like a dog 18 hours a day and she starved more often than I care to remember. The whole catastrophe. This caused her to exert a lot of control.
When I actually think about it I am amazed at how she did it. As a mum I can see what her motivation was. Us, her children.
I left home in a teenage rage at 17 (she was 37) and our relationship was forever damaged IMHO because of her overbearing sense of entitlement - always delivered tied up with a pretty bow, not ugly and direct.
THAT was what I rebelled about. I didn't drink. I didn't smoke. I didn't do drugs. I didn't have sex. I raged against the control. More than in your average teen-angst kind of way.
I felt/feel that there was always an implication that I owed a debt to her. That is not conducive to a very nice or rewarding relationship for either of us.
We reconnected mildly when I was about 23 and she and I rugswept all of the ugliness that had gone on.
I am 38 now and she is still in my life but I don't feel close to her. I think she thinks we are and she still tries to cross boundaries with me but I am super firm.
She has cooled it off these last 5 years because she is VERY keen to be around my girls so we each tread kind of lightly around each other.
It may sound unpleasant it is not - she is a devoted, doting and delightful grandmother.
I honestly could not wish for a better grandmother for my children. It is quite astonishing really as she wasn't a very pleasant parent.
Not because of the situation we were in because I've seen these situations bring families close. But because she resented me, us - her kids.
I don't do things because she thinks I should. The debt I owe her is too big to ever repay and quite frankly I don't remember signing up for it. I was a child. She did what she had to do. I am grateful for it but I do not consider it a debt that I owe her.
My sister is 8 years younger and hasn't spoken to my mum in over 5 years. They are completely estranged. The control was far more subtle with her youngest child but it was always still there.
I know this is an extreme case but I see elements of this a lot between mothers and daughters.
I want one of those relationships where I can talk to my mum anytime about anything and she can talk to me but we just don't have it. I never will.
Please stop focussing on Christmas and how your parents are going to feel.
That is a symptom - not the disease. What is going on? What happens when you try to talk to them? Have you guys been to therapy together?
Why is your relationship stiff? What part in it is yours?