As soon as a custody complaint is filed, the Court will issue a standing order prohibiting either parent from removing the child from Alaska without permission from the Court or the other parent.
If you would like to move out of state with your children before the case is resolved, you will need to get the other parent's consent, or file a Motion with the Court, requesting permission to leave the state with the children.
It is important that you do not simply leave the state with the children - even on vacation - while there is a case pending. Doing so could be considered custodial interference, which is a crime of domestic violence in Alaska. You could face criminal prosecution, or lose custody of your children.
You should also know that the court determins custody based on the best interested of the child, because many of the best interest factors favor stability for the children, leaving the state permanently might work against you unless can give good reasons to the court.