What can I do if my husband was awarded temporary custody over a year ago and final hearing keeps getting postponed by the courts?

I would consult with your attorney, and if you do not have one, engage one. You are correct that the longer the current custodial arrangement is in place a more difficult it is to have it significantly modified.

Do you have an attorney? If so, then chances are the case is going as fast as possible. If you don't, getting an attorney would be helpful.

Whatever reasons you have to argue that the temporary order should be changed, can go before the court on a motion. If you have anything substantial, make a motion. Otherwise, it's likely the temporary order will become a final order.

Unreasonable continuances in custody matters are contrary to public policy but common in some courts (especially LA). If the continuance was for a custody-related reason such as allowing time for a custody evaluation, you seem to have no choice. However, if it was just a court scheduling matter, your only alternative to waiting would seem to be bringing an ex parte application for an order shortening time, citing the law that provides that custody has priority over every other matter on the court's calendar except domestic violence. So if the court has divorce matters scheduled ahead of yours, you can insist on being given those dates. If the court is only hearing other custody cases, you are stuck. Usually, a judge will resist efforts to insist on the priority. Then it is a question of how much you are willing to aggravate the judge who, in the end, is the person who makes the decision about the final custody order. This is tricky stuff. An attorney would be a good idea at this point.

You need to be represented by an attorney if all the postponements are going. It should make the matter go more quickly.