tanith
Insist ‘Gertys’ Mum goes too so she can clean up the inevitable mess.
This would be my immediate response too, but I am not certain that my quondam headmistress would have approved it!
Is there any possibility of seating Gerty on her own, so she only vomits on hersefl the floor and the empty seat beside her? (Bad enough, but better than over other children).
Knowing today's parents and their dear, spoiled children, who are in no way responsible for their lack of upbringing, I very much doubt that whether you are a teacher taking a class on a trip, or a volunteer planning supervised events for children during the holidays, whilst parents are at work, that you can actually either demand a child takes medication, or ban the child from taking part.
This situation strikes me, a retired teacher, as a minefield, so before proclaiming ulitmatiums, check whether you can and may do so for your own sake.
I imagine your strongest allies are the parents of the children who were within Gerty's range.