We have had this issue as my eldest child is divorced and his ex has always insisted she has the children on Christmas Day. We had them once before Christmas, did presents on Christmas Eve morning as the children were being collected later that day. Never did it this way again as it just upset me for the actual Christmas Day a feeling compounded when the ex posted 'wonderful' (sarcastic tone) photos of the best Christmas ever of them all + new partner on Facebook!
After that I decided we'd do it our way, so FC still comes to ours on Christmas Eve, leaves the presents under the tree, we Facetime to let them know he's been; then we have our family Christmas Day on the 27th and the kids and our eldest stay over. Its our tradition now and it works well!
I decided that its only a date after all, me and 'Im indoors' have a quiet Christmas Day pleasing ourselves as to what we do, eat, watch etc- relax on Boxing Day while getting sorted for the fun and mayhem to come the following day
Good Luck and hope you get something sorted which suits everyone. Not easy I know.