I would schedule a meeting with her teacher maybe while recess or something. The only way that it is going to get resolved, and it is faster, and will most likely make you feel better about it.
Sending a letter, or email is impersonal especially if this is a important issue to you, and I agree. You can go in, say what is on your mind and see what she has to say, and it gets the real story clarified.
Hand washing is so important, especially these days. The children go outside, and get dirt and mud on their hands sanitizer isnt going to cut it. Same with using the bathroom, touching other kid's hands etc, etc. Hand washing is necessary! No buts about it.
I cant remember how many times I wash my hands everyday. Its endless, I could imagine it should be the same for the children. They are smaller, and their immune systems are too. They get sick so often that is should be mandatory for them to wash their hands when they get to school, bathroom breaks, after coming inside from play on and on.
Its one way of protecting our kids from germs and such. I dont understand how a teacher can refuse to let them wash.
Go in, and explain to the teacher all that, and that your daughter cannot use hand sanitizer due to her allergic reaction to it. I am allergic too and cant use it. It dries my hands out so badly that they are rough, dry, cracked, and rashy. Its painful. Washing with soap and water is more effective.
Good luck and hope it works out.