Do you agree with me or parent and child?

If it is a youth organisation you are not compelled to take her on any future trips.
It is most unpleasant for other passengers if someone has vomited: the smell lingers and can make others feel ill, not to mention the damage caused to upholstery and carpet in the vehicle.

In order for Gerty to have choice she caused great discomfort to the children on whom she vomited. Not to mention the smell to be endured by everyone. No one else on the coach had a choice to not be involved with the consequences of Gerty's selfish choice. The mother needs to understand that actions have consequences, sometimes very unpleasant (for other people) as a result of her indulgence of her own child.

It's totally unfair on everyone .
Either Gerty takes a tablet or she doesn't go or her mother comes as well with a bucket just in case and cleans up any mess .

As another member said it should come under the heading of ‘safeguarding’ which I agree with. A child who vomits could inhale said vomit and choke or another child could get up and slip in the vomit thereby injuring themselves, or another child could feel ill after being vomited on. Putting it under that heading would cover the OP inasmuch as insisting this child either takes a med or comes with a responsible parent who will bring along suitable containers and cleaning substances to deal with this problem.

i was a sahm so i would go on the days out with my childs class, i made sure he was in another group with another person who was helping, it was never a problem. i would tell gertys mum that she comes or gerty does not go if she does not take the medication, make sure you have a plastic bag and she has to hold it at all times and be sick into that, if possible she sits on her own, it might seem harsh but being sick on someone is not funny.

When I was young, I was always feeling sick when travelling, and was very grateful for an anti sickness tablet.

It is perfectly fine to give a child choices, this is how they make decisions after all and the earlier choices are given the better. Particularly with regards to bodily autonomy, however, the consequences of decisions need to be discussed. In this situation when you’re just presented with it, sitting at the front away from friends but with a bucket would have been my solution. Going forward, she’s not allowed unless tablets have been taken. And then make sure she’s sitting with a bucket.

Entitlement is the name of the game.