Well, I am now experiencing new behaviors! I decided that since I know the owner of these horses (no new horses have been to her barn and none have been off the property in over 30 days) that I would go ahead and see what happened when opened the area between the paddocks so that they could have access to each other. What a shock! Haley had been the "prima dona" at the barn she was foaled in and in the barn she lived in from age 1-5. She was adjusting to being a normal horse at our barn, but my other gelding was not an alpha at all, so Haley was still #1 in their herd. She has always been an angel as soon as you put her halter on or have her under saddle.
Well, Haley advanced toward the new gelding (Thunder) to establish her dominance, and Thunder told her that she was quite mistaken. She has yet to submit to him, but now, when she tries to stop moving, he starts following her until he has her running again. She is now so confused! For the first time in her life, she has found a horse who will not back down to her. Instead of trying to dominate me, she is now on the run from Thunder and looking to me for protection. Needless to say, Thunder is calm and cool, and Haley is hot and sweaty. Thunder may have solved the problem.