If the judge denies a request for custody, does s/he have to explain why it was denied?
Yes. Anytime the judge makes a custody arrangement that both parents do not agree on, the court must specifically explain why "on the record." Usually, the judge explains the reasons orally, in the courtroom. The denial of custody should be documented in an order but the reasons for the decision are rarely explained there. If you would like the judge's explanation and you cannot be in court to hear it, you may order a transcript of the oral decision from the court for a cost.*
* NJSA § 9:2-4(f)