This all depends on is the divorce mutual agreeable in which case the Bais Din will rubber stamp the Civil Courts decision although I know of one case when they didn’t. The couple had remarried 3 times and was trying for the fourth time to get divorced. The Bais Din said they needed long term counseling not a get.
If the divorce is contested and either party wants reconciliation and is given time to reconcile. If the time elapsed and they are not reconciled They go back to Bais Din and can request additional time to reconcile. If they are still not reconciled by the allotted time then I think the husband should get a Toyan which is a lawyer for Jewish Court. He will advocate for you and will present your case in the best light.At this point evidence is presented and witnesses are cross examined by both parties and the case is judge and a verdict is eventually is issued. A Siruv is the equivalent of a Contempt of Court and is issued when the losing party doesn’t follow their ruling. It is only issued if the winner agrees to pay the Jewish Courts’s legal fees if they are sued in Civil Court.