On the flip side of things, I want to tell you Gilda that I think you're doing a great job as a professor (from what I can tell!).
You are being extraordinarily kind... that's why I think you should come down a bit harder and not enable the girl.
I am on the other side of this issue in that I am a TA, and my professor (also my PhD advisor) does NOT have his shit together. And unfortunately, I am not in the position of power that you have, where you can call your TA on the carpet. I cannot call my superior on anything.
Minor vent: he has me covering over two weeks of his absences in class this semester, and one of those weeks he did not even tell me about beforehand. I had to pull together lesson plans at the last minute, and then I find out he wants me to grade all the papers they are turning in (not just daily work, but I'm talking major papers that will count for large parts of their grade). I told him, "No, I am not grading those on my own, that's not fair to the students because I know they are writing for you and not for me." I told him I would grade them in pencil and let him at least look over them and comment before returning them to the students. He also asks me to dog-sit for him whenever he's out of town, without any kind of remuneration (this is even when I am a not his TA). It is a VERY unbalanced relationship, but I feel powerless to change any dynamics of the situation because of how much status he has over me.
So, I guess I am writing (and venting) to affirm you, Gilda, in that you are exercising your status in a just manner. I encourage you to continue using your status in that manner, and not to feel uncomfortable about giving this girl a reality check.