As well written as this letter is I think you have left her in complete control of saying "no, I want to nurse in the daycare".

I think you might need to be clear, you can email but you need to say that her presence in the daycare is setting your child off and in order to keep a calm and smooth running program you need to have her nurse outside of the daycare. Let her know that you are willing to still allow her to nurse before leaving, but that it will have to be upstairs out of the program.

This will show that you know what is best for your daycare, and therefore know what is best when her child is in your care as well. It also makes it clear that your child's behavior is a result of her presence...you made it seem like you weren't sure why he was acting up, when you clearly do.