I finally managed to enter to that house. This is how I did:
1- I started a New Game+ without reseting my high Defilement/H-Experience.
2- After Elise opens the gate to Lower City at day 1, go back to church ASAP.
3- Talk to Elise and she will talk about a kid with a curse in that two-story house.
4- Now the two-story house is unlocked.
I don't know yet if you can do it on a New Game or a New Game+ without defiliment. But hey! now is something!
I didn't do it on Day 1-2 but I still can't do this. I've done the Old Lady retrieving the Amulet and helping the Young Woman with her Sleep problems.
I have like 150+ Defilement and stuff and have been chatting with Elise almost daily pressing every button I could. Nothing.
Now I'm stuck on this one... ??
Edit: I got to the Old Rosary, and now she's just saying "Oh, I don't know of anything work mentioning at the moment."
I suppose this means it requires a lower defilement rating OR it's a day 1 or 2 kind of thing.
I'll check once I get a bad end (if I do...?)
Edit: Finished the game, nice. It seems the Tutoring requires you to NOT have High Defilement. I had more than 100 defilement probably, which is likely how much you have when you are considered to have "High Defilement".
If anyone needs help with the game in terms of playing it, ask me. I do not know how to solve any crashes.