This is a tough one. My niece has a terrible peanut allergy AND she is homeschooled. Not for that reason, but it IS the reason she doesn't go to many outings with other friends. We all have to be very careful. My kids don't like peanut butter so when we're around them it's pretty easy. But she has jumped into my car at their house - and I had peanut M&M's in there. Luckily, I told her she needed to get out and there was no reaction.
I think that it is okay to have a "no peanut" rule at the school. And refined peanut oil is usually okay for folks with peanut allergies, just not unrefined which is more organic, etc, and probably not used in many things? I do think it's okay for the kids to have to wash hands, etc, upon arrival at school but not after lunch and all day long.
My heart goes out to her and her family - and I think the other parents need to figure out another solution with the school. If the district doesn't watch out, they could find themselves in a lawsuit, especially if a court rules that she is discriminated against b/c of a disability.