I wish people would stop suggesting that spending a day other than Thanksgiving or Christmas with family is going to miraculously make everyone happy. If there is already an issue, then I seriously doubt that anyone concerned is going to be adult enough to spend the holiday on an alternate day and not be petty about it.
Sure, I can spend Christmas Eve with my mom and sister and then stay home with my two babies and husband Christmas Day (which I plan to do), but I'm never going to hear the end of it from Mom and Sis. They give me grief about this every single year.
Answer: Outrage is in the eye of the beholder, I guess; I interpret different-day suggestions as consolation prizes, not miracles.
But even if there were a way to make everyone happy, that might not be ideal. The annual mother-and-sister guilt display needs to be banished to the attic, and they won't do that if it keeps rewarding them with what they want: your presence, and if they can't have that, your validation. Just by getting worked up, you reassure them their rigid holiday expectations are legit.
Since the whole issue is your Christmas Day plan, you first need to make clear that it's not open to discussion. Your plans are with your husband and babies, this year and for the foreseeable future, yes?
Then say so. Then, let them know what you can offer: the Christmas Eve consolation prize.
Then, believe in your choice. Let Mom and Sis know you won't apologize for honoring your own priorities. "Since I can't be in both places, I've chosen what's best for my family." Repeat, verbatim, as needed - for you, mostly. You really can hear the end of it: "I love you, we're not discussing this, goodbye."