Legal Question in Family Law in North Carolina

Yes it is possible to appeal. Appeals are (a) very costly and (b) very unsuccessful. You have to demonstrate to the appeals court that not only did the trial court screw up but that the screw up was so bad that the appeals court must send the case back to start over. Appeals judges do not really like to get involved in domestic stuff. As long as the trial court's order is basically fair, then it will not be disturbed absent something really egregious. I cannot conclude based on your brief facts whether there is anything appealable or not.

I am not sure that trying to get new counsel on the eve of a hearing is the way to go. Its completely within the discretion of the trial judge to grant a continuance. You do not indicate why new counsel was needed. Did you fire old counsel? Why? Or did counsel get sick or die or something like that? It might make a difference. If you just fired counsel then it was your decision but the court does not have to hold up proceedings because you caused your own problem. If prior counsel could not work on the case, then it might be an abuse of discretion because its not your fault.

Your appeal runs from the final order of the trial court. As an alternative to an appeal, why not wait till the court enters its order (meanwhile get new counsel to look it over) and if something is really really glaring, file post trial motions to have the trial court consider the points that are wrong? Post trial motions will delay the need for a quick appeal and will allow the court to correct any real errors. Then the appeal would run, if needed, from the order denying your post-trial motion.