Go ahead and put up the electric. You can even use wire. Entice her to reach over the fence to reach a pail of treats you will be holding. She'll touch it once, get a good zap, and do the fastest turnback ever. I doubt she'll challenge the fence after that. They can sense when the charger is on. If she's already been behind electric in her earlier life she'll know what it means. It only takes once to teach them.
A friend of mine has that problem with her clyde x, who looks more like an overgrown pitbull on steroids.
She has gone over the fences, so they made them higher... Then she would just bulldoze through them, so she had a strand of electric wire tied to her chest, after she got shocked from that she stopped going through the fences.... And started going under them... So now we have to find a solution for that.
I hope your horse isnt like that one!! It's a right pain