It is correct to first try and correct her with leg, and then turn her in a small circle i f that doesn't work. You want to give her a chance to respond to your aids properly, and then need to correct her in a constructive way without making her angry or scared. Because a trail ride for an "arena horse" is a stressful thing already, we want to avoid unnecessary use of force, like a whip or spurs because they may scare or anger the horse more than they would in the horse's normal situation. You are also right that the last thing we want is a rear, which is why as quickly as possible we must get the horse from backwards movement to forwards movement. It is extremely difficult for a horse to rear if they are going forward.
So yes, circles are the correct thing to do, and even put in a transition to trot and back down to walk. Enforce that she must not go backwards unless asked to, and when asked to move forward again, she must oblige, but do it in a tactful way without making her scared or angry.