Cale, this whole situation is sad (especially for the poor horse!) and happens more than you can imagine. If I had $5.00 for every person I knew who bought a horse on a whim and ended up with disaster, I could afford to support many more than I currently have!
Chances are, your ex-girlfriend will not change her ways and will continue to buy the wrong horse and then dump them when they don't work out. It sounds like you were at least trying to do the right thing with the lessons and a bit of training help but any experienced horseperson here will tell you that a green, 3 year old horse is completely unsuitable for beginners. Those relaxing, mosey trail rides that you imagined come with years of training and a novice should buy a horse already nicely trained to fulfill that dream.
This is a harsh lesson and it's one I've warned all of my lesson students about, usually to no avail; Don't allow yourself to get emotionally invested in an animal you don't and can't own-you have no control over what happens to them.
I myself learned this the hard way as a young teen and it about killed me.
If you truly care for this particular horse, see if you can buy her and continue your lessons and training help on your own. That doesn't mean "get back with the girlfriend", this is something you can do on your own with some good help. You also have the option of finding an older, completely trained trail horse, join a trail riding club and "live the dream"!
You will (as an added benefit) meet a lot of nice ladies in the horse world where men are in short supply!