My monster's school also have a Shanghainess teacher who teaches the kids Chinese, she speaks n understand little English, she is firm with the kids, no nonsense when the kids are in her class. Even my playful mischievous monster also sits down quietly listening to her. When other teachers could not handle my monster (who has a really bad temper n is more stubborn then a cow) they will ask her to help lol.
Kids are not suppose to play or wanders away from their class otherwise chaos will be every where, the teacher did the right thing by moving her to her class. Perhaps its the shock of a stranger carrying her that makes your girl cry? Perhaps the teacher should talk to your girl while picking her up, at least she gets your girl's attention.
Anyway a gesture may be seen differently by individual. A firm hold of the hand to get the kid's attention may deem to be rough handling to others.