Hmm, I still wonder what exactly Rin's trauma is. I know we saw something of it in Episode 12 of Refrain, but not sure how much of that could be Tonokawa/Shimada making stuff up... Riki's line in an earlier episode about Rin being pushed around by adults wasn't even in the VN either, so let's ignore the anime.
We know that the scene that happened at the end of Rin 2 echoed Rin's childhood trauma in some way. In Episode: Rin, Rin mentions a dark room, huge people, and screams. Whose screams exactly isn't clear... she also mentions to Riki that some people pressed her down when she was a child.
(This is why I doubt the anime is accurate. There weren't even any screams in that scene... and where did those adults even come from anyway? They were all men too for some reason. Why were there a bunch of men hanging around picking on a six year old... I don't get it.)
There are also these lines in Episode: Kyousuke,
There's no point whatsoever in living a life full of hardship and misery.
Rin, you out of everyone should know that well.
That distant day, when you learned how scary living can be.
Ever since then, the two of us have been walking together.
Parental absenteeism does seem to be a thing for that matter. That line does kind of imply that it's been just the two of them ever since that day, when something scary happened. Kyousuke also makes a pretty big deal out of Riki taking care of Rin in his place, as if there's nobody else to look after her.
There's a bit more on that in the Kanata route (this is from the seen file in Fluffy's repository)
"The reason Kyousuke wasn't going to college... that was probably for Rin's sake."
Kyousuke's trying so hard to get a job as soon as he can, probably so he can pay for Rin to go through college, and even keep supporting her after that. It seriously does seem like their parents aren't around.
It would probably be safe to assume this trauma involved something happening with their parents. I think their parents are still alive though. If Kyousuke and Rin were also orphans like Riki, I'm sure that would be mentioned. Rin mentions her parents pretty casually in her route too (even for Rin, I think casually mentioning dead parents would be a bit of a stretch)
Eh, people on Japanese sites are talking about how the song "Hanabi" has a connection to the Natsume siblings? Um, but Hanabi was made before Little Busters. Though Maeda wrote the lyrics and he might have had some story in mind when he wrote the lyrics, which he adapted into the Natsume siblings' backstory, I guess. It's possible.
Now that I think about it, it does make sense, with lyrics like 'The increasing number of cats you gathered was worrisome' I'll analyse it another time, maybe.
There's stuff about it here: http://cocktaileffect.blog104.fc2.com/blog-entry-6.html
Wow, I just realized, those blog posts were written in 2007... way before the anime aired, let alone Hanabi being used as an insert song.