We alternated Christmas day & Boxing day each year, with handover around 10am Boxing day which worked for us.
I absolutely had our "Christmas day" when the kids were with me.
I did a variety of things on actual Christmas day if I didn't have the kids, depending on my situation at the time.
One year when they were small I just told them it was Christmas day a couple of days early and we celebrated it then, apart from that they knew it wasn't "Christmas Day", but it was the day we treated as Christmas, we spent it with my parents, exchanged presents etc.
They had no objections to having a repeat on Boxing day with the other side of their family.
As a child we always celebrated both Christmas day and Boxing day with my parents, sibling, maternal grandparents and their 2 younger sons who weren't that much older than us.
The two days were pretty much identical other than Christmas day was the present exchange day. Depending on what shifts my dad was working, one day would be at our house and the other at my grandparents.
As they got older I think their dad did his "repeat" day a couple of days later rather than the next day.
Oh, and my dad was an arse when I did the earlier day, said he wasn't exchanging presents till the actual Christmas day etc. My mum told him not to be such a pain, and since then he's not said anything.