The other bit is that the sketch is likely portraying Kyou, but if that's the case we have to believe the daughter can't recognize her mom. Now, if she was a toddler, MAYBE that could happen, but this seems pretty far fetched (so it's probably what the author is going for, given the track-record). People usually take pictures as well, and I knew from a young age what my mom looked like as a kid, teenager and young adult (maybe this is a point for the "adopted daughter" theory? But even then it sounds like she would have been with Kyou for a long time). Again, this would be less annoying if it wasn't one of the few "narrative developments" that are coming out of this chapter.
I think Midori collecting the drawings and enjoying them as potential surprises with each grocery list is cute, so kudos to the author for coming up with the idea. The fact that she is a gluttonous, daifuku-fueled "guest" is also kind of funny (I guess that comes from Kyou).
Where is this going? Probably nowhere. I need my dose of nonsensical plot points, damn it!