Appealing a Temporary Order
It's not usually possible to appeal a temporary divorce order, because it's already subject to change in your final decree. Your efforts might be better spent making sure the temporary order doesn't carry over to your decree. You can do this by going to trial and mounting a case that proves you're the more appropriate parent, so the court will consider moving your children from your spouse's home to yours because it's in their best interests.
You might be able to modify your temporary order rather than appeal it. The rules for this vary a great deal from state to state. In South Carolina, you can file a motion for reconsideration, but the judge might not take kindly to your argument that he made a mistake when he issued the first order. If circumstances have changed since the temporary order was entered, you can instead file a motion for modification to bring this to the attention of the court. Some states are more lenient than others about modifying temporary orders. For example, you don't have to establish that there's been a change of circumstances in Illinois.