Dealing with the appellate court can be very difficult. In fact there are attorneys who specifically work in the area of appeals. I would suggest you meet with a few appellate attorneys for help before it is too late.
To answer your question, yes the rules allow appellate courts to grant relief and extend deadlines under these types of situations. In fact, our appellate courts tend to grant such relief many more times than they deny it; because it sees its role as resolving cases on the merits and not on technicalities (with some limitations not germane to your facts).
If, as you say, your ex has retained an appellate specialist who used to work for the court, you are well advised to reciprocate and retain someone similar.
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No. The Court of Appeals may grant additional time to file a brief at their discretion, and as the other attorneys pointed out, the extension is almost automatic unless some type of undue prejudice is shown. Based on the facts given there is none. I would also advise you seek appellate counsel.
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