Well I sort of half agree with Charroit and half agree with everyone else. In my experience, horses have amazing senses of humor - they like to have a good laugh every now and then. I always get a kick out of seasoned trail horse that they use at Dude Ranches and the like because the cowboys will say the horse is bombproof, and anybody can ride them, but when an inexperienced rider is on their back, they do little things just for fun. They'll crow hop playfully or toss their head every once in a while. They'd never hurt the rider because they know better, but they're bored of walking the same route over and over, and they sure do get a good chuckle out of the rider panicking and saying, "Um... excuse me! My horse is crazy or something!" (Also, I'm not saying that Charriot is inexperienced - my comment was on horses being bored, lol.)
Maybe you guys have never had that experience.
My opinion is that horses get bored, and look for other ways to amuse themselves, be it antagonizing another horse or an inexperienced rider, or something more mundane like chewing on their halter/lead rope, or cribbing.
They're very similar to children in a lot of ways.
So, while I agree with Charroit that her horse might be getting a good kick out of spooking the other horse, it's my opinion that she's bored with walking the trails. You say she doesn't do it when she's "dancing" (a term I'm not familiar with, but it clearly isn't walking) so that leads me to believe that she's bored. HOWEVER, I do agree that this is a dismissal of your authority - you've asked her to walk, and she should. So I have to suggest doing some groundwork or lunging pre-trail ride, to establish that you're the boss on this ride. It may be something she already knows, but, and this happens with kids too (can you tell I work with kids a lot?), she may feel like you two are buddies, and she can push your boundaries. Doing a bit of ground prep before a ride might remind her that you're in charge.
Also try a change of scenery. I know when I take my horse (who HATES to walk - she looooves to go!) on a new trail, she walks quiet and is paying attention to ME - she doesn't know this place, and is trusting me to keep her safe and to direct her where to go.
I think people forget far too often that horses have senses of humor - we need to keep them amused!
I hope this helps. :]