does a judge usually go with the one parent that showed up for the court ordered mediation in a child custody case?

The legal standard is best interest of the child. I would suggest that there is no data to support one way or the other that the first parent that shows up at a mediation is the custody awardee.

Good luck.

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You won't win by your husband's default but his not showing up won't endear him to the judge either. Common sense and experience tells me that his no showing up for a court ordered mediation will help you in the custody battle. Since I don't now any other facts there is no way I could predict who might win.