The thing to remember is that you need to stay as professional and mature as possible. Everything should be "please" and "thank you". Not "Shut Up!" - not even - "Quiet" Try "Quiet, Please". You might be surprised. ("Shut Up, please" doesn't count)
The fact that your director is making a "kid" (pardon my French

) do the work that she as a teacher should be doing is part of the problem. When it comes to "yelling at the cast" be careful. What I can say from my work with guys your age is the second you start "yelling" you sound like one of the teachers that everyone hates.
Also young-adults tend to think that they can "guilt" a cast into working for them by using sarcasm, or other off the cuff comments... it won't work. It'll push away the kids that don't respond to you and it might cause those that are responding to stop.
We've all had "those" actors and trust me it doesn't stop in high school, I do alot of work with mixed cast of young adult, children and adults and the last show I worked on the 7th grader in the cast was more mature and professional then a 24 year old in the cast. At one point or another you have to be able to say "I've done everything I could, I'm just going to do my job and that's it."
All in all remember that the cast takes it's queues from you, in more ways that one, if you come to rehearsal all bummed out and making like things are gonna suck... guess what...
Break a leg and keep us posted!