Daughter and son-in-law not happy with each other

You don't say if you are cooking Christmas day, if so this could complicate things. Do you have a partner?
I was thinking you could take control of the little one and purchase some suitable toys which you both could play with while your SIL and daughter go out for a couple of hours and they might try and come to a compromise for the day.
Having time as a couple if both are working can be hard work on a relationship this could give them a little breathing space to talk.
There are lots of alternatives to this, your other half could cook or your daughter, you could just prepare a buffet to make it easier than a full Christmas lunch. Most of this could be prepared the day before.

I agree with Silverlining48 about a walk. Fresh air and exercise rarely cause rows. Otherwise can you suggest they go out together while you look after the little boy? Maybe a couple of hours on their own might help them relax.

I think you need to be careful not to be seen taking sides. Telling sil to go to his parents is a definite no no for me. You really need a little chat with both parents to say let’s put aside differences and be nice to each other over Christmas and make sure gs has a lovely day with good memories.

I agree with Allsorts poor child having parents sniping! I would have a word with your daughter , sounds as though they are both as bad as each other, really must put their little child first I really hope they sort out their differences of opinions not just for Christmas but for the future and certainly not fair on the little one, I hope you have a calm Christmas Dotty

This is obviously going to spoil the day for everyone so I would do as Freshair suggests and tell your son-in-law to spend the day with his own family.

Selfish pair. The child will be picking up on it but they know that. I wouldn't say anything to parents, your comments will not be welcome. I would give my attention to the little boy, Christmas is for children and he will be excited so give him time. Arrange a couple of little suprises for for him once they start.

It's just one day.

I would only address this if something happens in the moment. Tread carefully here.

Does your SIL have to be there? Can't he go to his parents instead. You deserve a nice day.

Sympathize with you but they do need to be told about the detrimental effect on the poor child as Christmas is a magical time for young children isn't it? Are you brave enough to confront them tho,?
Difficult situation.

I'm tempted to agree with pascal but what about the child?

Having a word with your D is a good idea and I hope the day isn't spoiled for you but at least if they are with you, your GC has a better chance of a happy day.

Maybe you could talk to them both and point out that their constant arguing is having a detrimental affect on their child.

Can’t help, sorry, but in a similar position so sympathise.
It’s just a day. If weather permits go out for a walk, the fresh air will tire the toddler and they may even leave early….

I would have a word with your daughter and get her to agree to a truce with her husband just for the day. No sniping and no bad feelings.. If they can't agree to do that for the sake of their son and for you I would cancel hosting them..