I do think you are being unreasonable. And believe me when I tell you, dsd and I had some ROUGH patches when she was growing up, especially around 10-11 y.o. landmark.The bad news.
You are in it together - you and your partner. She is his daughter, and you can't pose ultimatums to father regarding his child. I just can't imagine telling DP "I'm done, you are on your own". We stop being a family at that point. (at least that's how I see it)The good news.
You are in it together - you and your partner. Yes, she has a father, and yes, she can be an unreasonable, maybe even selfish kid, but she is now YOUR unreasonable selfish kid, kwim?
Your husband has to recognize that your role is a lot harder than his. If you tell him "this hurts me, we struggle with this, and this needs to be resolved," then you AND your husband need to come up with a solution that will help you to raise a child you committed to. He has to be committed to it as much as you are. It won't work otherwise.
Here is what I would continue doing.
*picking up when needed
*making lunches, dinners, snacks and favorite cookies, etc.
*offering without expectations: "Do you want to pick up a movie from the library?", "Do you want to make cookies with me?", "Do you want to play with us?"
*ask a quick "How are you doing?", ask "are you okay?" if I suspect she is hurt, or doesn't feel well.
Here I would stop doing.
* any form of discipline. Transfer this responsibility to your husband for now. This means everything - you don't tell her to clean her toys, or to make her bed, you don't tell her to eat her snack. You take care of her, but you don't discipline, you don't send her to her room when she is rude. This is where your husband has to do his part.
* expecting instant change. It took us years(!) to find balance and harmony in this family. It started with a fact that I realized that dsd's opinion of me is changing as time goes by, and I can choose to act differently - she will respond differently.
* I would also stop trying to involve her into things too hard. You offer once, and go about your business. She will want to participate in fun things, and if you don't make it a requirement, she will think twice "huh! that looks like fun!" Once she is the one asking to join you, she accepts the fact that fun stops when she doesn't behave nicely.
* don't insist on long conversations with her. Kids naturally want to tell things, BUT when you try to get "tell me about your day, how is school" from a kid that is having trouble accepting you, they get annoyed. Instead, try to say as little as possible. Let her set the pace of how often she wants to tell you things, and how much she wants to talk.
* Don't feel defensive.
I guarantee your dsd is worried that you are taking her father away. She is jealous of all the time you get with him and she doesn't. This means two things - she needs to spend more time one-on-one with her dad (and that's up to him to realize and work it out), even an ice-cream place once a week woudl be great for just the two of them.
You and your husband need to recommit to this together. I think you should distance yourself, but in a different way than you are describing. You should take a step back and allow her to approach YOU as often as possible, vs. you trying to make it work.
I do speak from experience. We had a nightmare of a situation at some point over here. Then about 2 years ago I did exactly what I am suggesting for you to do.