Mab wants to change Harry, Molly does not.
But helping Harry to keep himself together? Of course. It is good to feel guilt and responsibility when it is proper to do so but it should not make it impossible to meet your current responsibilities.
That is my whole point, we know from the past that Harry can be a bit of a drama queen when it comes to taking the blame for something.. He will beat himself up to the point of destruction, Molly is doing what she can to ease that with some sound advice as well. I think Molly is doing this on her own authority as Winter Lady, not under Mab's orders... However at the same time if she was opposed to Molly doing this it wouldn't happen.
I don't think Molly's planning to live at the house she's buying in her parents' neighborhood. The way she framed it was as a way to have her own faerie goons keep an eye on the house and protect them without them knowing about it.
I don't think she is planning on spending much time at the apartment either. Harry was in the process of moving in with Maggie in Jury Duty, I seriously doubt he'd do that if Molly was always there... 1]her parents wouldn't like it,2] I doubt that Mab would like it, 3] it could get complicated if he sees a lot of Murphy..
I think it's more the Cold Case sense of gift giving; she paid the bills because she felt it was a good and necessary gesture, not to assuage Harry's guilt. In other words, she framed it as an obligation and thereby got away with it.
Yeah, but at the same time she said all the death etc wasn't his doing, and that his words in the aftermath saved a lot of people... That isn't in the Cold Case sense of gift giving..