I'm the mother of an only child. So I see the situation from the other point of view.
Adult child their partner and I have lived together for about 25 years, their choice, but I welcomed it.
I never presume they will spend Xmas with me. Although adult child's partner is the youngest of six, I'm aware that I get the majority of both their time. So I leave it to them.
this year the two of them are going to partners Mum before xmas, and they are cooking a Xmas meal and exchanging presents two weeks before xmas. Partners Mum will be with three of her other children on Xmas day.
adult child, partner and I will have Xmas day together.
when they've chosen to be at partners Mum on Xmas day, they know I'm just fine with this and we celebrate and give gifts on their return.
the thing is, they decide. And they do it knowing neither mum is going to get offended.
So, I'd say to the opening poster, that they should do whatever they wish to do. If either family takes offense, that's on them, not on you.
Oh, and I should say that neither Mothers in this scenario are capable of travelling to each other. we are too Far apart, distance wise, and too old to manage it.