What should I do?

Thank you all so much for your input which has helped me to go forward and sort it out.
As Nannarose said was it my sister who actually witnessed the event or was it second hand information from my mother. That I will ascertain by asking my sister directly. Then I can put this ridiculous episode in the rubbish bin where it belongs.

The original remark may also have been meant kindly - we often gently tease a friend who always gets up to help and look after everyone!
But whenever an elderly person seems to be misunderstanding / saying strange things, I always wonder about dementia (and yes, I know it isn't always the province of the elderly!)
You don't say if your sister said she observed your DiL's behaviour, or if she is reporting what she was told by your mother. If the latter, then I would keep an eye on her,and (although I know some would disagree) quietly mention to close family that Mum seems to getting a bit muddled and saying odd things, please be aware.
I'd add that the 2 incidents are very typical of early dementia: meaning to say something and it coming out wrong, and forgetting that you have seen /spoken to someone.

Tell your sister to stop stirring up trouble. She is at the root of this and needs a good verbal kick up her derriere.

Do you think your mother is trying to to stir up trouble by complaining to the family? Why would she do this? Does she dislike DIL?

The original comment was pretty rude. I cannot quite decide whether your mother was implying that it was up to DIL to do "women's work" or whether she was implying that DIL was somehow inferior and that the maid/skivvy tasks should come naturally to her.

My grandmother makes comments like this to me all the time, usually I do call her out on it, not rudely, just stating that times have changed etc, as I don't want DD being influenced by the 'women's work' comments.

You seem to get on very well with you DIL and clearly know her well and have proof she didn't keep your GD away from your mother, so really I only see 2 options

- your sister dislikes your DIL and has made it up to get you to dislike her, which is barmy and a bit far fetched as going by your OP it doesn't seem like they see each other very often

-or secondly, your mother doesn't like your DIL and has been complaining about her to your sister, this seems a bit more likely to me. How is your mothers relationship with your DIL? And with your son?

I find it all a bit strange like why someone would take such offence at a remark from an old woman (I guess in her day it was woman's work, women always did the cooking and cleaning?) DIL didn't need to make an issue of it really. Why would you bother?

Then don't understand why your sister has suddenly after so long brought it all up again?

Also don't understand why she was 'distant and edgy with you. Are you sure there isn't more to this? If not, non of it makes any kind of sense so I would ignore it all.

Stuff and nonsense and not worth bothering about, if they have a problem let them sort it out.

I don't see why your sister should be distant and edgy with you. It doesn't sound (and you have photographic evidence) that your DIL did anything wrong. Even if she had done something wrong, it wouldn't be your fault.

Yes, I think your sister is in the wrong. If your relationship with her is usually good, could you perhaps ring her and say you don't like quarrels and could you go and see her and talk about it rationally. Take the photo with you.

Perhaps your sister could visit you so you are on home territory.

I don't understand why your DIL was cross at what your mother said to her in the first place.

What a strange situation, although it does seem your DIL took umbrage as you say from an innocent remark from your elderly Mother last year.
I would shrug the whole thing off if I were you, all these sensitivities floating around are just not worth worrying about.Certainly don’t repeat what your sister told you to any other family member.Nowt as queer as folk eh?

Do you mean using rather than abusing? I think that you should take the photos of your mother and your Granddaughter to your sister and just tell her , nicely, that she must have misunderstood the situation and you have
The photos to prove it!
It seems that as your DIL has moved on from the remark made by your Mother( which was extremely rude, but maybe allowances were made because of her age) then the rest of the family should forget it too.
If your sister mentions it again, then maybe a quiet word asking her what she is up to might be in order?