I don't see the issue with wanting Christmas morning just with your partner and children.
That is exactly what we are doing this year. It's our first Christmas living together, and my DP live on the other side of town so we are having breakfast at home, then popping to my DP at lunch, then to my partner's bro and SIL for dinner where I think we will see more of his family.
I've done all sorts over the years, having friends stay over for Xmas day, staying at others for Xmas day, home hopping ON Xmas day, staying home the whole day, we even stayed at my XH's with my newborn (DD2), newborn's dad and half brother, because my DD1 lived with my XH at that time. Stayed with family, friends.
There's many ways to skin a donkey, but I do think that sometimes it's nice to have the xmas morning to yourselves, specially so that you don't have to rush around getting ready for someone. Being able to take your time on what can be one of the most stressful days of the year, is important to me, for sure. I have fms and m.e among other things, so not having people in my face at my home is better and helps enable me to be more prepared for socialising later in the day.
My XH's nan was rude like your MIL, and would also turn up unannounced all the time, specially when D1 was fresh home from the hospital. Shoving her camera in her face when I'd just gotten her to sleep and all sorts. Saying whatever she felt like saying, whoever it hurt. So I've been there - it's hard to tell a matriarchal figure how you feel, this one I had to put up with was the kind to take serious offense to everything. So if it was her trying to come round first thing, I'd be miffed and asking to make it later at least.
We all have a right to organise Christmas our own way and we have a right not to have someone insulting and rude under our roof. Your DH isn't being very kind to you over this.