Indulge me while I overthink things a bit more
Specifically about the changes to Mat and the Cauthons.
Mat mentions being a horsetrader in ep 3, and he tries to drive a bargain with Fain in ep 1 like he’s accustomed to bartering (so maybe his claim has a basis in truth and isn’t just an attempt to impress Dana). Is it possible they haven’t dramatically changed Mat’s backstory at all, that the Cauthons
were affluent and well respected, but have been broken by grief and Abell lost it all?
The E5 kids aren’t just aged up, the inference is that the timeline has passed along enough for Perrin to have married Laila (like book-Perrin said he had once intended, as Asc pointed out). Could the Cauthons have lost a daughter in this extra time? The little girls have the names given for Mat’s sisters in the books, but there is also an inconsistency in how many sisters book Mat says he has (which I think was just a mistake on RJ’s part, but anyway). The show’s writers might have used that to canonically justify an unnamed sister.
Both Natti and Abell’s behaviour looks like it could stem from grief to me. The girls are both shown to love their mother and usually sleep with their parents at night, in fact they generally seem pretty happy and well-adjusted. Mat clearly shields them from the worst of the neglect -- they think mum is sick, and they aren’t afraid of her outbursts, so it doesn’t seem to me she’s like it all the time. The show really focuses in on the loss and reflection part of Bel Tine (the show’s rituals actually seem to have more in common with something like samhain than beltane). Whatever the specifics, the Cauthons have clearly lost
someone, and recently enough that Bel Tine is still more painful than comforting for them. It seems Natti’s way to cope that night is to get drunk, while Abell buries his head.
I don’t think the village (or Nynaeve) would just tolerate Natti and Abell being shitty parents and shitty people. It’s one of the main criticisms I’ve seen for the change. The effects of grief would be viewed differently by the rest of the village, though.
It might also be significant that Natti’s braid is super short and a little ragged, like maybe she’s cut it off. There’s nothing to suggest cutting hair is a ritual of loss for women in the Two Rivers, but we do know women’s braids are significant. Nearly every other adult woman we see has very long waist-length hair.
Rand and Perrin chip in specifically for lanterns for the girls, and we later learn they are used as part of a tradition of guiding departed souls back home. There’s a peddler’s wagon full of potential treats for two little girls, but the boys clearly know why Mat was gambling for funds the previous night. Even Fain seems to know he will want 3, Mat doesn’t ask for them, he asks for money (I think he was hoping to buy the lanterns
and make some coin from the bracelet he stole. Funnily enough given Perrin’s declaration that they’ve noticed Mat’s lack of luck, his friends give him the money after he already has lanterns. So maybe he’s not quite as unlucky as it seems because he actually got exactly what he wanted).
The first of Mat’s lanterns is actually given over by him to Natti. Tam’s voiceover is specifically at the part where he talks about dealing with heartbreak, and “even death”. When he goes on to say that the Wheel keeps turning “always” we see Natti launch the lantern, and then the shot focuses on Mat and the girls while Tam talks about trying to do better the next time. I think they chose those shots very purposefully to tie them with the words (they also seem to choose very particular shots when Moiraine tells the Manetheren story so I’m assuming it's intentional).
If Mat had lost a sister, it would also add extra weight to his scene comforting Perrin. The focus is on Perrin’s loss, but Mat seems in a ton of pain himself. Why would Laila have given him a knife? And not just that, but the story that went alongside it. As book readers we know that tools v weapons is a huge motif for Perrin’s character conflict, so it makes sense for him to hear it. But ignore that for a second, and consider why Laila said it to Mat at all? Here is a gift, a practical tool (because Laila always made tools not weapons), but
also something you might use in the future to protect someone you love. Why make that distinction? It sounds a lot like someone trying to offer comfort: here is something to make you feel in control, a talisman against future loss.
I’m not sure that any of that, if it’s even remotely correct, will ever come up in the show (although, man, if when we return to the Two Rivers we see that the Cauthons have rebuilt themselves like the Manetheren of old, that will be a sweet pay-off. It might also be a way they help Perrin to address and process his own grief and ability to move on when he goes home, because they
do need to address it somehow and not just use it as a way to illustrate his conflict with violence). In any case it’s interesting to think how show Mat’s changes might also have been rooted in the books.
As to what might have happened to this sister, another thing I didn’t quite understand was Bran’s reaction to Egwene’s return after the ceremony, because while Marin is ready to celebrate and all the women are cheering, he is visibly worried -- like he thought something bad might have happened to her. We know the men aren’t privy to the whole ritual, and nor did we probably see it all, but it seemed odd. Being chucked from cliffs aside, Bran doesn’t
know what the ceremony involves in order to be worried about it. I really doubt women routinely die during it, that would make it stupid and risky. So why would he be afraid? Unless an accident had happened in a past ceremony, in which his best friend had lost a daughter.
The other suggestion might be that she was a channeler. In the books Bode is much closer to Mat in age, and goes to the Tower to train, so if they used that as a template in the show perhaps she had the spark (rather than just having the ability to be taught), and because everything is happening a little later she died of the Sickness.