The AG hearings (99% of them) are held before a Master. He isn't an elected Judge. Because of this, you can appeal his decision any time within three days after the final hearing (see section 201.015 of the Texas Family Code). Up until September 2013, the time limit was seven days.
In fact, the Master is supposed to tell you about this at the time of your hearing, in open court.
How Do I File an Appeal?
You have to do three things: (1) create a Notice of Appeal and (2) file it with the District Clerk's Office and (3) send copies to the other two parties.
Remember that there are THREE parties in your case:
1. The Mom
2. The Dad
3. The State of Texas (represented by the Attorney General)
Any party can file a three-day appeal - Mom, Dad, or the Attorney General.
You may disagree with the Master's ruling because he didn't hold your ex-husband in contempt; because he made a finding of an arrearage amount that you think is incorrect; because he set the monthly payback amount too low; because (in a paternity case) you wanted retroactive child support, and it was denied, or it was granted in an amount that's too small; because the Master set child support too low (you KNOW the Dad is making lots of money, but he lied in Court about it); because the Judge allowed too much visitation for your ex-husband. FILE AN APPEAL. You do NOT need the Attorney General's permission to do this! Remember, they don't represent you.
Did the Judge order you to go directly to jail? Did the bailiff put handcuffs on you right there in the courtroom? Did the mother of your children do a little victory dance? File an appeal. By law [see section 201.1042(c) of the Texas Family Code], you must be brought before a real (elected) judge on or before the next working day after you file your appeal.
In non-jail cases (that is, the Judge DIDN'T order you to jail):
After the appeal is filed, the Real Court (the one with the elected Judge) will notify you by mail of when the appeal hearing is set. When you get your hearing before the Real (elected) Judge, you get a second bite at the apple, so to speak. The appeal hearing (which is held only on those specific issues that you complained about in the Notice of Appeal - be sure you're thorough!) is by "trial de novo," which means you can testify, call witnesses, present documents, etc., as if the first hearing had never happened.