And I just have to add, when no food is involved, the risk of a reaction is minuscule. It makes absolutely no sense to exclude a child with food allergies when no food will be present. And, since you will be on site at the same time, in the very unlikely event of a reaction, they could have you administer the epi-pen to your daughter.
Epi-pens are designed to be used by laypersons with no medical training. It really is no different than administering the Heimlich maneuver to a child who is choking. Is BFS willing to allow its volunteers to administer the Heimlich maneuver, or would that also be asking too much of them???