If any child gets seriously hurt to the point that they require medical care - yes you stay until their parent or medical help arrives if you are the only adult.

That is the basics of being a human being - nothing to do with being a nanny.

I would hope Ds' nanny would help another child who was seriously hurt. And by help I mean contact their parents, get help from someone in the school, or if need be, called 911. I'd be pretty horrified if she just walked away saying "oh well this punk isnt my responsibility and he shouldnt be here without a parent. Plus my charges have to get to a class. Im sure the other kids can figure out what to do"

What kind of hurt are we talking? A bruise and skinned knee? A broken bone?

I still say if a kid is swearing around your charge, you need to relax. Focus on the kids in your care.