The smoking (mainly) and drinking secondly (seems like she's almost an alcoholic) is what put me off her.
I haven't seen her sincerely apologize ( I could be wrong, but I remember her saying something like "I should apologise" which is not the same as saying "I apologize" or "I'm sorry") It's a small techinical detail but means a lot to me. One is her saying it because she knows it's the right thing to do, but doesn't truly want to, the other is her doing it because she wants.
And don't forget she's still hiding the fact she's Emy from him, which as I've said several times it the thing I can't forgive her for.
IMO she's barely started down the right path. As you said she moved in his house several days ago and unlike the others trying to make ammends, she went straight back to the bullying tactic of calling him "Piggy". Lucky for her the dev is writing the story and not me, because she would have been out on the pavement less than 60 seconds after she said that the first time.
After MC told her what happened in the past,she was deeply touched and apologized to MC. This conversation happened in EP6.
Emma:"I never actually sincerely said 'sorry' to you before."
Emma:"So with all the things I did in the past..."
Emma:"I'm deeply sorry, [mc]. Please forgive me."
MC:"Uhm... Please raise your head, you don't really need to bow, you know?"
MC:"And please stop talking to me so formally."
Emma:"I want to make it up to you, so please give me the chance to do so. But... I have no idea what to do right now, so please give me time to think about it."
Her hiding all those things surely bothers me as well,but I do understand her for not saying it right away. But MC discovered it himself anyway,so we'll see what will happen in EP7.
As for the piggy thing,yeah,that's her fault.I won't argue. She claimed that even calling MC by his name was too much for her,but she shouldn't had called him piggy. At least just saying "you" would do. But as she said,she will make it up. So we'll see about that.