Well, if Grandma won't let you move, you may have to get kicked out. How you choose to do that is your choice, and I'll admit that it doesn't sound like a good idea. But if you did it right, you might swing it okay.
Another way would be to put a nail between your Grandma's friendship with the barn buddy. Tell her some hateful lie or something about what the barn buddy said behind her back. (I feel awful even typing this, but if it were my horse, I'd do ANYTHING to get him/her out of there!) Grandma may not believe you at first, but Grandma sounds a bit selfish and needs a swift kick in the rear, from the sound of it. Eventually Grandma will probably resent the barn buddy, and will support your decision to move.
These are low-ball tactics, of course. But if you really want to move your horse, you'll find some way to get her to agree to it.