What happens if a judge requires both parties in a chils custody case to go to mediation but one of the parents doesn’t agree and won’t mediate at all?
You need to file a motion to enforce the mediation and make an alternative request that the case be set for a final hearing.  The speed of the setting on your motion will depend on the court docket of the judge.  It will talk longer if the judge carries a lot of cases; and, conversely, will go quickly if he has an efficiently run docket.  Regardless, the sooner you advise the court of her refusal, then sooner you can get your cases moving and resolved.