As my forum name states, I shoot left but I' m right handed and left eye dominant. As a kid starting off, my father determined I was left eye dominant and made me always shoot left handed with both eyes open. However I was not a bowhunter as a kid so I feel for your struggle with this girl because she cannot pull the bow back left handed.
Many posters have stated they are left eye dominant but close that eye when shooting right handed. I would think that is the only way you could shoot right handed since the dominant eye will ALWAYS take over if left open. God made us that way.
It was real easy for my dad to help me determine. I cannot just close my left eye, only my right eye so in the beginning I was having fits trying to sight in with both eyes open and shooting right handed.
So it seems you have two options: 1) Strengthen her arm over time and have her shoot left handed/left eye dominant and be able to shoot with both eyes open or 2) Shoot right handed and close her left eye.
You do lose some depth perception when you close one eye so my vote would have been option #1 but gee, I might just be a little bias!!!