Made it through Week 3!
I also took note of 育子’s UV ray concerns. I burn easily, so my initial thought was that she’s relatable. I think you’re right about it being something that’s meant to stand out, @Phryne. If there was maybe just the one mention of it when they were going out to lunch, I might not have thought much of it, but with the previous mentions of it included, I think it was a purposeful choice by Murata-sensei. I have some ideas of what it could represent, but nothing concrete so far.
I agree with people’s sentiments here over who the sister wants to kill. My first inclination was either the mother or 育子, but because a lot of the drawings in that sketchbook were of children, I wonder if she’ll go for ミサキ. There are parallels between her and the sister; 育子 mentions that both are smart, they have “interests” that are grotesque (no judgment for eating イナゴ, but it did make 育子 want to puke, so it can probably be considered gross within the text). There’s also the connection between the sister and ミサキ from when she was a little girl. I don’t know if the story will get into it or not, but those are just my thoughts on the possibilities.
@jhol613 brings up a good point about the more nefarious side of this system. It definitely runs the risk of feeding into people’s darker thoughts and desires, such as those expressed by the sister. The system focuses on the cold, hard numbers: more people are born than killed, so it’s good for humanity. However, the quality of life for the children born under it is left to be whatever it is once they leave the center. The culture that manifests itself from the system (in this case, mothers feeling more attached to children they birth themselves, while being more distant from those they adopt) only really has the front-facing rule of “it’s a good thing, and the people who become Birthers are doing a good thing.” The section mentions it’d only been going on for 30 years at the time of 育子’s memory, so it’s still relatively young enough that the effects of it on people’s mental health and other aspects may not be well known. Or, the mother should know better and not say things that could harm her children. Probably a bit of both. I wonder if those taking children from the center are well-vetted before they’re allowed to do so or not. 
@AmomentOfMusic I’m in the same camp as you, though 育子 may be pushed into a corner before relenting. Also, I’ve been adding page numbers to the Google sheet as I’ve been catching up, so no worries there.