You know what, @childlessstepmom - I was in exactly your situation, and I felt almost exactly the same, about SDC, about DP.
Reader... I married him. From feeling huge resentment about SDC, I grew to love them enormously, almost as much as my own (newish) DC - the kids love each other too.
All these feelings - seeing an ex partner in the children, wanting more 'couple' time, feeling guilty that you aren't instantly in love with someone else's children, even really dread their presence sometimes - I'd say they're normal, particularly in the early years of a relationship. But relationships change, and in my experience, step children can sometimes even make things better, particularly when you're over the just wanting to lie in bed all day stage (it does pass...). There's so much silliness here about how horrible step mums are if they don't think all the 'right' things about their SDC, and how they should leave immediately to vacate the place for someone better - a lot of it does come from people who've had bad experiences themselves, so I don't discount it. But it isn't universal truth.
I'd say, give yourself a break. Get to know your SDD, take an interest in her. Ask her questions about her life, get chatting. Accept that she's there. Accept that your feelings are fine - all of your feelings - as long as you act like an adult and are kind to the children, who don't have a choice. Your feelings aren't you, and neither are your thoughts - what matters to others is what you do. 9 year olds are fantastic. They turn into 11 year olds, and 16 year olds, and they grow up and leave home (by which time you might well be very sad to see them go). Life is a long business, and it always changes.
Whatever you decide, good luck with it. But the bit about you really loving this man but finding life hard really struck a chord with me - I could tell you all sorts of things that were exactly the same for me in the beginning (and it wasn't easy for him either, and we disagreed and fought and had situations where neither of us was right or wrong and we both ended up in tears). But we've all learned a lot from it, and I love my whole big family these days - never more so than when we're all together. When I had my own DC I thought 'my' complete family would consist of them and DH. But it doesn't. If SDC aren't there, there's a hole. And 6 years ago, I never ever ever would have thought I could possibly think that.
Good luck!