The only set I'd go to on Christmas Day are the devout, committed Christians. Anyone who isn't shouldn't be fussing and crying about seeing grandchildren on a particular day within what is, of course, a TWELVE DAY festival. And a committed Christian would never use emotional blackmail, surely!
Four visits in one day is frankly nuts and you do not need to contemplate even attempting it. It is a bit late now to accomplish emigration before Christmas but I'd seriously consider it for 2020.
Meantime, how about this?
Dear Family, After discussing it, DH and I have decided this year not to chop our Christmas Day into four equal chunks and spend it rushing about, wrangling small children in and out of their carseats, driving, and trying to enjoy your company with one eye perpetually on the clock.
After all, Christmas has twelve days!
We would like to suggest that you each nominate a day from the list of dates below (insert list leaving out 25th itself and including about 8 dates if you can) to invite us over. First to request a specific listed date will be accepted. You can include your second or third more choice in order of preference if you like.
On Christmas Day itself we plan to celebrate simply at home so the children can explore and enjoy their presents.
We think this arrangement will be much more relaxing and fun for everyone - let's spread the joy!
You could message it at a time you know they will all be available to see it.
You could even offer a couple of 'open house' dates when they could come to you, but that might be an alternative for next year if you're not already settled in Australia/Canada/Darkest Peru!
Good luck. Take control. Enjoy.