There quite a few threads on here regarding this behavior so you may want to search barn sour, or herd bound. Since your only 14 I would highly recommend finding a knowledgeable experienced adult to help you. The issue your dealing with can be fixed easy enough but can also escalate quickly if your not sure what your doing. The most important thing is keep yourself safe while you learn how to work with your horse.
But basically if her fence is high enough that she cannot get out don't worry about her running around and bucking and whinnying she needs to learn to get over it on her own. As for you riding her out on own, or making her leave the pony she needs to know you are the leader and look to you for safety. Doing lots of ground work is a good place to start. Start by working her near the pony, longing doing lots of direction changes, yield her hind end, yield her front end, do lots of backing, what ever you do make her feet hustle trot and canter get control of her feet and enforce that you are in charge. When she is wanting air take her a little ways from the pony and let her rest with you. Rub her, groom her make being with you a good a place to be. If she gets excited about getting back to the pony take her back and work her some more. Eventually she will learn that being with the pony means work, being away from the pony means rest. You can tie her in a safe place and let her stand for awhile as well, just leave her until she is standing quiet.
The same principle works for riding when you ride her out make her feet work do circles, serpentines, shoulder in shoulder out, lots of lateral work get her thinking about you so she does not have time to think about the pony.
Horses are herd animals so even though she may not like the pony much and sounds like she is in charge she is worried about leaving the pony, safety in numbers. Alpha horses worry about losing their leadership status while they are gone. She needs to know that when she is with you, you are the alpha leader and she needs to listen to you, and you will keep her safe.
In short go back to basics with her on the ground, get control of her feet and the problems will take care of themselves.