How can a minor speak to a judge during a custody battle?

A:Short version is “you can’t.”  There are ethical rules about “ex parte” conversations — i.e., one side of a case (or a witness) speaking to the court outside of the presence of the other party.  However, at 16 you are almost certainly in the zone of minors entitled to have input into custody decisions affecting them — the full statutes, including those rules, are posted (with lots of other material) here.  It is possible to arrange for a “child interview” of even younger children in a case, if relevant, through the Family Mediation Center.  But it is unclear how or why your mom “can’t get a hearing.”  Really, she needs to confer with a qualified family law specialist, who should be able to answer all her questions.