Well, that's where you and I differ.
If I was in an absolute lose-lose situation to be killed be an assassin, where I had to die with no way out of it, then I'd be choosing asphyxiation than say....... getting my throat slit with a knife (given both are extremely painful methods, I'd rather die with my body intact lol).
You're assessing all that dismissing "Rina didn't mean to kill herself and MC" theory based on one big assumption that Rina didn't use the dosage meant for kill.
And that very short segment of flashback in (or anywhere else in the game) nowhere at all does it indicate she intentionally short changing the dosage.
In fact, what she literally says to child MC when she tells her "Mom, it hurts" is the following:
View attachment 3668737
Dunno about you, but that line pretty much feels to me of words a mother comforting her son, knowing full well she is willingly taking her own son with her to her grave (and she says "soon" too, implying soon enough poison will claim her son's life).
And very shortly after that flashback memory ends.
Given it's a very short flashback, basically anything could have happened to interrupt the process; Cordia, Wilfred, & Rina's ex-fiance could have bursted open the door saving Rina and MC in a nick of time (i.e. outside factor interupting the suicide attempt).
Also, MC in the flashback's stage is a kid.
Instead of Rina literally stabbing or slitting her own son with a knife and his last memory of his mother being that she stabbed him, she very well could have wanted a death for her son with his last memory being that his mom still loved him (to avoid sullying his memory of her).
Hence, the whole comforting she does to MC.
MC as a kid didn't know his mom was trying to kill him, cause it's much less obvious than something like a knife or a gun or anything with quick death etc.
I'm not saying what I'm saying is what really happened, just that it can very much be a possibility and not dismissing the whole possibility cause I find it pretty plausible and wouldn't really contradict Rina's character even if it happened that way.
On the other hand, what you said could possibly be correct and she could have shortened the dosage on purpose (even though as I'm saying before, I prefer the former that Rina actually did mean to kill both her and MC lol); and as I said, I have been wrong before.
It's just that it seems you're dismissing the alternative to your theory too quickly (citing it's not consistent), especially given there's nothing really shown in the game to contradict it until now, nor would it be inconsistent with Rina's behavior as not just a Serpent, but also a mother.