The word "threaten" in this context is correct. When you tell someone, "Do [something] or I will [do something that negatively affects you]." You are threatening them with that action.
Definition of "Threaten"...
- From Merriam-Webster:
- 2a: to give signs or warning of : PORTEND
"the clouds threatened rain"
- 3: to announce as intended or possible
"the workers threatened a strike"
- From Cambridge Dictionary:
- [ T ]
to warn of something unpleasant or unwanted:
"She threatened legal action against the newspaper"
I don't think anyone here has suggested that the man threatened these children with violence, and if he had said what he did to the children's guardian (ineffective as she might appear) he would have retained much of the moral superiority he thought he had in addressing the minors.
Instead he made the impotent gesture of yelling at kids, telling them to do something he's incapable of forcing them to do himself on the
threat of going to get someone else to make them if they refuse. Call it whatever else you like but that is exactly what the OP describes.