About getting dizzy, instead of turning constantly, walk a small circle while facing her or even slightly ahead of her, and if you want to stand in one spot, turn halfway, pause, turn halfway pause, rather than constant turning. Looking only at the horse helps, don't be tempting to look beyond at the horizon going by... and by and by...
The stopping is deendant on how you have her hooked up. Using a chain under her jaw, you can pull and it puts pressure there. Just snapped onto a halter, body language and verbal are about the best you can hope for. Stepping "behind" and giving a sharp pull while giving the verbal also can help. Shaking a lunge whip in front for the determined lunging horse to distract them from the repetive motion and make them pay attention to you, and/or the surroundings sometimes works. They can get "bewitched" by the round and round too, and the shaking of the object in front of them usually breaks that trance(if your animal is prone to it).