as he always knew she would, and he was quite happy to send her away in "Doomsday"

We clearly have very different definitions of what a 'happy' expression is. This may explain much of our confusion with each other.

Do I agree that having Rose there helped the Doctor handle the pain of genocide? Yes, much in the way that having my mother there helped me when my aunt died. I still had to work through the pain and she didn't fix anything, but I don't view her as an 'emotional band-aid' either.