Robyn, I have not yet seen the show, but from what I've read, it seems like Alyssa exhibits some very positive signs of being able to improve in some areas of concern. For instance, it sounds like she behaves fairly well in other settings, is able to interact appropriately with others, etc., that most of her acting out and expression of such negative feelings comes at home, with you... strangely, that can be a GOOD sign; it may indicate that after a day of working hard to control herself, she feels secure enough with you to "let down and relax," so to speak.
I taught students with behavior disorders for many years, and I can't tell you how many times that happened... kid is assigned to my class, causes all kids of chaos, I might actually see a decline in behavior, I start thinking I am actually a negative influence on him; then the regular ed teachers start getting back to me with "Whatever you're doing with him, keep it up; he's a different child! Way to go!"
Eventually, when the appropriate behavior becomes easier to manage and they don't have to expend so much energy away from home, the home life will settle down, too.
Hope that helps a little...
; )