Hi, I'm profoundly deaf, never learned ASL (but really want to) and my mother told me that when I was almost 4, around the time I got my first hearing aids, that I threw a lot of temper tantrums and had constant fits of rage - and this continued throughout elementary school. I am totally empathetic with your child - it's not easy being a deaf child trying to live in a hearing world, in a hearing family going to a hearing school. It's not easy to witness everyone communicating with ease when you are struggling so hard to fit in with them.
I'm really glad though that my parents did not opt for me to get Cochlear Implants - that should be my choice, not theirs. And for the record, I will be turning 40 soon and I still refuse to get CIs. And if I had deaf children, I would never make them get CIs. Hearing Aids and CIs will never be good enough substitute for ASL - i speak very well and people are often stunned to find out I'm profoundly deaf - which is not a compliment and in fact, makes my life even more difficult because they assume if I can speak that well, then I can hear that well and I can't! i'm still left out of conservatons at my own family's dinner table because I can't follow all those people talking at once. I have two teenaged sons and I can't follow their conversations at the table either and have to constantly remind them that I'm at the table too.
But I will tell you something, my mother was my rock growing up and it was of great comfort to have her love and support during those horrible years going to a hearing elementary school. Let your child have her temper tantrums and wait for her to calm down, give her big hugs and LISTEN to what she's trying to tell you. If you really want to know what it's like to be in her world, get some ear plugs and try to follow what everyone is saying at the table during supper time. Then you will know why she's so angry and frustrated.