The biggest challenges often come in small packages

I was just writing to my family, and realized that I have more sympathetic ears than I normally take advantage of. I'm sure all you teachers in particular can relate. Here's what I was writing...the background is that I teach in an inner city school, and though many, if not most of the kids have problems, this one student has severe issues (has-tortured-animals kinds of issues).
She is a little girl I lovingly refer to as "my runt." She got passed around from class to class, and even school to school, until she ended up with me. Well, on an average day, she is simply annoying and disruptive. As I feared, her presence has completely altered the dynamic of my classroom. She certainly functions far better with us than she has anywhere else, but unfortunately, because of her, we are noticeably less efficient than we used to be. Even considering the other trouble kids, we were building a system that worked for us. Still, everyone needs a home, a place to feel welcome, and I am more than happy to provide this place for her. But it is so difficult! She doesn't do herself any favors, either. She creates conflict and is a constant disruption and distraction. She is not emotionally in touch, so she feels no guilt or remorse... imagine trying to discipline and mold her behavior so that she can be successful! Without a doubt one of my most challenging tasks. Thankfully, she will finally receive her psychological consultation in a couple of weeks. I truly hope it leads to her receiving the services she needs, because even though I know I am a significant and positive presence for her, she needs more than I can give her. Anyway, point being, I had to be so hard on her today. I spoke more forcefully than I've had to speak to any child, or any person for that matter. She was completely out of control, and I knew I had to do it, but I literally had to brace myself. Even though they were just a few words, they took so much out of me. I let her sit in the office alone until the end of the day (devastating for her, because she thrives on attention). When I picked her up she acknowledged her words and actions, and apologized and promised she would never behave that way again. Sadly, I've heard it all many times before. I told her I accepted her apology, but I wasn't sure I believed her anymore. She says tomorrow she's going to show me that she means it.
I'm trying to remain hopeful. I hate feeling this jaded.