She wanted Emily to be condemned as a criminal for crimes she hadn't committed, so that's why she didn't try to kill her. As for why she didn't try to kill Emily's son, I assume that maybe she doesn't want to murder a child? (That, and it'd have been too dramatic a theme for the story the author wanted to write.)
I disagree with your interpretation that a stepfather is automatically a father figure, though to be fair I don't remember how old he's supposed to be (obviously he wouldn't react the same way if he was five or eight - I don't think he was written as older than that). Dick would be the third replacement father figure, but the fourth on the whole.
Okay, I don't remember the "deliberately". Dick's a friendly person, so it seemed rather natural to me. Obviously, since you find the premise of the story flawed, you're going to find his behaviour with the child at best insensitive, since he's not thinking about the future all that much; but I think it's worth keeping in mind that in the story he's at first attempting to unmask Emily and then protecting/proving her as an innocent, so in that way he's already being concerned about the kid. I'll need to reread.
On the subject on them not sleeping in the same bed, I always thought Emily thought Dick was gay, and she respected that either he couldn't tell her either he hadn't admitted it himself. It made a lot more sense to me than their abandonment issue discussion. (About your mention of Emily being needy: that scene was the closest the story came to stating it, but I thought that discussion made it fairly obvious. So it's implied at that point.)