If the teacher hadn't gotten involved, and something bad had resulted, then everyone would be screaming that a teacher was right there and did nothing. So I do think she has right to get involved in she sees a problem with a student from her school on a field trip.
Now if it was at the grocery store after school hours, I would feel differently about that.
If I were the teacher, and the parent was completely handling the situation on the field trip, I would have probably just kept an eye on the situation and not done anything unless it caused a problem.
If I was the parent, I wouldn't be mad at the teacher, I would be mad at my kids for doing something wrong. Even if I disagreed with how the teacher handled it.