I go through the motions of what I know a parent is supposed to provide her child. I do the things, buy the stuff, spend the time, ask the questions, try to engage. And I feel none of it. I know the difference because his father and I have our own biological children now, and what my heart feels for my own is everything that I don't feel for my stepson.
I think the first thing you both need to do, though, is to adjust your attitudes in the situation. I know this sounds a bit accusatory, but hear me out. You describe Emma, who is a child, as a "spoiled brat." You don't just see her behavior as bratty, but her personality as bratty and somewhat irredeemable. Children can pick up on when they aren't liked, and-like it or not-when you married Diana, you also made a commitment to Emma that includes being there.