"Her mom allows her to do what she wants and 90% of the time she is left on her own at home because mom is out running with friends."
These are your words. Do I need to say any more? She is a pubescent teenage girl with an unformed brain, and you are an adult. She needs love, even when she's unlovable. At this age, is it often all one-way, and you don't get much back from them for years.
If you are loving to her, despite the fact that she is not very lovable right now, she will come around eventually. You need to do the right thing, even when she doesn't. Like I said, YOU are the adult. Don't criticize her, praise her. Keep sending her pictures, but respect her silly whims about not being in them. Go shopping with her and help steer her towards hip, yet more appropriate clothing.
It sounds like overall you've tried to do right by her, but you need to keep trying, despite the fact that you don't feel like it.
How would you like to be in her place, with a divorced family and a self-absorbed mother who doesn't pay any attention to you?
It's not wrong of you to dread her visits, but it IS wrong of you to act out on those feelings. You can make a difference in this girl's life. She needs love and approval and acceptance. Do it.
p.s. -- If you don't do this, and you think it's bad now, just WAIT four or five years. If you think there's stress on your family now...
By the way, love works way better than "discipline" (man I'm sick of that word).