My XH seems to wangle his shifts so that the DCs are with him either the night before or the night OF their birthdays, so they wake up at one house, get their presents and go to school, then the other parent collects from school and spends the evening.
Sometimes we all go out to eat with other family members or if they are having a party with friends we won't get together.
This year DD was home with me before school, then at XH's after school, stayed overnight and then had friends here the following day as it was the weekend.
I try not to make too much of it, it's just a date, for me the special time is the day you celebrate.
Similarly, they are all at their dad's tonight. They will stay there and all come round in the morning. Other people think this is weird or must be hard, but for me, I will have a lovely day with them all tomorrow and their dad will get to do the mince pie for Santa and the stockings etc.
It's different, but it doesn't have to be horrible. I'm enjoying a peaceful evening, getting some tidying done and relaxing with a cuppa and a Christmas film.