Recently, I've been asked to flat a rather stubborn, somewhat unpredictable mare several times a week. The time that I have been asked to ride her coincides with a beginner lesson, and, as there is only one ring at my barn, we share the ring. However, the mare has the attention span of a rather energetic puppy; trotting around the ring will simply not do in her mind. Instead, she enjoys spooking at the cat that's been sleeping by the gate for the past twenty minutes, kicking the horse that's been riding up her tail, or bucking when asked to travel at a speed faster than a walk.
What are some exercises I can do with her to keep her attention focused on me, while not simultaneously disrupting the beginner lesson? Please keep in mind that not all of the students in that lesson have mastered the art of steering, and I would like to, if possible, avoid the possibility of the mare kicking another horse.