Kids can sense when you are having "mom guilt" and will try to milk it for all they can. A lot of single parents do exactly what you do, myself included - give give give, as if its some sort of compensation for their disrupted family unit. They begin to see a pattern of us giving when they are sad, and oh they will turn it on (not that they are never trully sad, they are, but sometimes it IS an act) because they know it will lead to "oh honey remember that new _____ you wanted, lets go get it!".
Thing is, most teenagers are moody and bratty and pushing boundries and daughters seem to hand it to their mothers the worse ( I have a son, and its a bit different). She is learning to manipulate you and its good that you are saying no sometimes, its hard I know, I hate to do it too. You know she has everything she needs, you know you have done and will continue to do the best you can for her, for her whole life and that should help you rest easy.
Times will be hard, she is trying to become independent of you right now but she can still assert this without disrespecting you and calling you names. She's had some dissapointments in her life, as many of us do - it doesn't give her the right to be cruel to you, the sooner she learns to see the positives , what she has instead of what all she doesn't she will start to appreciate you more.
Don't expect it any time soon, though Grin and bare it and welcome to the terrible teenage years ( the two's are nothing compared to this !!!)