L.L.
At six years old, it is a SHAME that her teacher is using letters and numbers on the notes. She is fully capable of learning properly. She will have to "unlearn" this bad habit, and her learning will start ALL OVER AGAIN once he "promotes" her to real music.
My suggestion would be to find a teacher that will teach her classical piano and isn't afraid to do it properly. I feel qualified to say this, considering I have been playing piano for 27 years, and need to quit typing to answer the door because I have a piano student here and it's 2 degrees below out!! ;)
I'm sorry she's had so many teachers, but I think another switch is in order. My daughter is 7 and can read real music and play with both hands. We all get discouraged, but with the proper teacher, she will easily overcome. If you have any more questions, please feel free to PM M..