Kids rarely eat their whole entree, so bringing them hungry won't make much of a difference from that standpoint. Don't let your kids wander around. It can be dangerous. Servers can be tripped and someone could be hurt by hot, flying food. Ask for a booth if they have them.
Kids can squirm around more, or be cornered if necessary.
Make sure your child is well rested. Don't bring kids just before nap time or bed time. For younger children, bring some of their favorite foods from home. Most restaurants won't mind. Bring food that can occupy them and keep your hands free for eating your own meal.