Can a third person file for divorce if husband and wife don't want it?

There is no procedure in Indian Law that a person (known or unknown) can file any case on behalf of anyone without Special Power of Attorny or Genral Power of Attorny. So as per your query / given information, your facebook friend can't file any divorce case on behalf of you or on behalf of your wife without any special power of attorny or Genral power of attorny executed by you or your wife in her favour to file the Divorce case.

Secondly, the passport size photograph of the party (who filed the Divorce case / petitioner) must be affixed with the petition and signature of the petitioner (Husband / wife) is mandatory on petition & the affidavit that is to be submitted alongwith.

In many Courts, the Hon'ble court requires the personal appereance of the petitioner.

So as per your information / query, the threat has no value, she has no right to send any kind of legal notice regarding this and no need to worry about break down of your family, she can not do that type of things but if you or your wife wants to take any legal action against her then you can file a complaint against her before the Police or the Court.