I guess if you want your wife to stay, you need to show more attention to your stepdaughter. If she lives with you, she's now your daughter whether you wanted that or not. You married into this and knew what you were getting into. If you're a custodial caregiver for a child and are together in the house and she doesn't live full time with her father, you're a father to her now as far as she's concerned unless she doesn't want that from you. She's a kid, and you're the adult; how would you like being a kid and the man who loves her mother doesn't seem to care about you? If you don't want to have a connection with her because she's not your biologically and your wife needs that and the child needs that, it's time for you to evaluate whether this was a relationship you should have gotten into, because when kids are involved the adults have to act like adults. Peace.
jam, I have a stepdad and in a lot of ways he is the perfect stepfather. The stepdad role is different than the dad role -- even if her biological dad has taken an interest, you have different shoes to fill. You've named some important responsibilities, like taking care of the financial end and the irritating hassle and cost of insurance, and a good man you are to do it. But, and it might amuse you to realize it, what a stepdad does best is not the hard stuff. What a stepdad does best, is be a cheering section and a sympathetic listener. Now, the examples I'm going to give are adult examples, so you'll have to translate them to what you can do when it's a 9-year-old. But my stepdad asks how I'm doing, and really means it. He is delighted by every brilliant thing I say (even when I know full well it's not brilliant). He LOVES my son. He praises my cooking and is impressed with my relaxed way in a kitchen. He laughs hard at every joke I make. He likes my dog. He listens sympathetically to my problems. He marvels at how fun it is to get together. Who wouldn't love that?
This programme is not one of lectures, parental instruction, or criticism. It instead is one more like "best friend." My mother has the right to be the critic, he only has the right to be a fan. But he does it so well that I adore him, and in fact, doubtless will take care of him in his old age.
My guess is, 9-year-olds are not that fascinating to you, and you see this child as "not yours" first and foremost. But she is your stepdaughter, and you can test your talent at being a friend, and an unconditional one at that. How many unconditional supporters do we have in our lives? NOT MANY. Give it a shot, asking her about one topic (such as how they use computers at school, or which of her friends like each other and what ones say things behind each other's backs) and you might find talking with her is surprisingly interesting. Never talk down, criticize or lecture -- only my birth dad could have gotten away with that and thank heavens he didn't do much. Just act interested.
A mom notices if you like her kid or not, and in fact loves you more if you do seem to like her kid because she herself loves the kid so much. As Paxiled says, if you don't want this gig, consider whether to stay in the marriage. But I'm here to say it really might be a lot easier than you think. Ask her about her hair, how she likes her style and what she thinks she might try in the future. Ask what kinds of nail polish she likes, and why. A little interest will go miles and miles. If it works, and you find your heart warming to the role of stepdad, your wife will reward you, too.