Is the dungeon unlocked already?
We checked the code just in case, but the only conditions to see Emily's dialogue options (in the morning when she's cleaning your room) are relationship 2 and the dungeon as such already being unlocked.
Well, and at the beginning of chapter 2 (first week), Iris must not be in the room at the same time.
If the dungeon isn't unlocked yet, you need to have seen Kate's first dream, then talked to Kate in her room about the dream, then go to the basement next morning where Kate will give you a short introduction.