You don't have to justify nor qualify yourself.
You have a prior booking to do work till mid-day. Their request for Xmas Eve lunch came well after you made that booking.
With things like this, first come, first served makes a lot of sense. If they can't see the sense in that it's their issue, not yours.
There may be some short term friction over this. But on the bright side, you should earn some respect from your girlfriend and her family on this. Because you do what you say you're going to do. You told your boss you'd work on the morning of the 24th, and that's what you're going to do, even though it's turned out awkward for you. With that being your general philosophy in life.
Ronseal man. You do what it says on the tin.
You're not fickle.
Seeing her family at Christmas and summer is better than not seeing them at all.
And I don't see it as a big issue if you join them for the main course and dessert. The main thing is that it's a chance to get together, have a chat and catch up.