Oh, it is always such fun to be sitting on a horse who spins with traffic—eek! The behavior can be modified, but it will take some time and patience.
We need to desensitize him around large oncoming vehicles. Right now, he likely becomes a bit nervous as he sees the vehicle, and then your niece likely responds by becoming tense (as she knows what is likely to happen next), which then makes her horse more anxious…you can see where this is going. Ideally, you will have a friend with a large vehicle (it might be a truck and horse trailer) who can assist.
Let’s first teach the horse to anticipate when a reward is coming. I suggest teaching him a food delivery sound (this is clicker training without the clicker). Simply pair a sound, like a whistle sound you make with your lips, with a small treat. Once he begins to look for the food to be delivered when he hears the whistle, you are ready to begin training him.
Now, let’s have your niece mount and walk him down a quiet road and have a small vehicle pass him. If he is calm—as he should be, based on your description of the behavior—whistle, treat and give a hearty scratch to his crest. Repeat until he “gets the game” and begins to anticipate the treat with the oncoming car. Now it is time for the friend with the big vehicle! First, under saddle, have your niece walk past the large vehicle while the vehicle is stopped on the side of the road. If he remains calm, whistle, treat and scratch. If he becomes anxious, simply walk him back and forth until he is relaxed, then whistle and treat. Now have the friend drive down the road very slowly. If the horse is calm, whistle and treat. If he is not, ignore the behavior and repeat the exercise until he is. Increase the vehicle’s speed and repeat the procedure. Finally, it would be great to add a couple more large vehicles to the same routine. Good luck!