What is the procedure to file an appeal on the judge of a family court case...
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You do not appeal a "judge." You appeal the judge's ruling if you disagree with it and if you have reason to appeal, i.e., if the judge did something incorrectly that warrants a new trial. Just because you disagree with the court's ruling does not mean that the judge acted erroneously. Appeals are very very expensive, time consuming and seldom result in a new trial.
If I were you, I would talk it over with your family law attorney. If you do not have one, then I would talk it over with a family law attorney and pay for the consult and for the attorney to review your case and see if you have any appealable issues.
For procedure, you have 30 days to file your notice of appeal with the trial court. The 30 days begins to run from the date the court's final order/decision is entered on the docket at the courthouse. You then have 10 days to make arrangements with the court report for transcription of the proceedings. Once the record is transcribed and delivered to you, you have 30 days to get your agreed upon record (you have to consult the opposing party or the opposing lawyer) filed with the appeals court. After the printed record is mailed to you, you have another 30 days to file an appeal brief. The case will then be either submitted on briefs or, if argument is granted (it seldom is), you will be notified. Case is heard about 9-12 months after the other side files its brief.
Read the appellate rules. They are your friend and outline all of the above steps. However, there are lots of tricks/traps that attorneys are aware of but non-attorneys are not. If you don't follow the rules the appeals court will dismiss your appeal without ever addressing the issues.