Last Christmas was our first with DD, all family were keen to see her on the day of course. We decided to stay put with an 'open door' policy to everyone, come visit anytime, we'll be here. Some came in the morning, others came in the afternoon, in all we had 2 visitors Xmas eve and about 16 on Xmas day, just visiting, didn't have to cook for anyone. Just cups of tea and Xmas treats to snack on.
We thought it worked great, everyone got to see DD if they wanted, no obligation if they had other plans, and we got family time on Boxing Day, just us. We have a big family between us so seemed fairest way. And DH only gets Xmas day and boxing day off so we get to make most of both days.
MIL has invited us to her house again this year (she invited us last year but explained above to her). I have thanked her very much saying we really appreciate invite but will do same as last year and likely that this is what we will probably do every year so it is fair (this was said openly last year that we thought it worked well and this is what we plan to do going forward).
AIBU to stick to this idea, I don't expect anyone to visit but they are all welcome if they wish.