On what halachic basis? To publicly embarrass someone?
You’re still repeating yourself. There’s a seruv against the husband, let’s say in our hypothetical situation. He has been declared by beis din to be in contempt. So action against him is authorized by beis din. Okay. Now you or some rabbi has the right to simply declare other people not party to the case to be impeding the process or even simply unhelpful in forcing him? Simply on the say-so of one person, and not a beis din where the third-party would at least have the right to deny or defend himself from such accusations?
There is no halachic basis ( you haven’t even attempted to justify it halachicly) and is simply an absurd assertion.